nanoelectronics and nanophotonics_mnt-301 unit-3_(ggct.pdf
TRANSCRIPT
![Page 1: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/1.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 127
08-11-2013
1
MNT-301Introduction to Quantum Computer
UNIT-3
The integrated circuit (IC) manufactured by optical
lithography
bull Silicon-based technology allows for the fabrication of electronic devices with high
reliability and of circuits with near-perfect precision
bull In fact the main challenges facing conventional IC technology are not so much in
making the devices but in interconnecting them and in managing power dissipation
bull IC miniaturization has provided the tools for imaging manipulating and modeling onthe nanometer scale These new capabilities have led to the discovery of new
physical phenomena which have been the basis for new device proposals
bull Advantages of nanodevices include low power high-packing densities and speed
bull While there has been significant attention paid to the physics and chemistry of
nanometer-scale device structures there has been less appreciation of the need for
new interconnection strategies for these new kinds of devices
bull In fact the key problem is not so much how to make individual devices but how to
interconnect them in appropriate circuit architectures
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 227
08-11-2013
2
Introduction to Nanocomputer architecture
bull Nanotechnology holds the promise of putting a trillion molecular-scale devices in a square
centimeter How does one assemble a trillion devices per square centimeter Moreover
this needs to be done quickly inexpensively and sufficiently reliably What does one do
with a trillion devices
bull If we assume that one can make them (and they actually work) how can this massive
amount of devices be harnessed for useful computation These questions highlight the
need for innovative nanoelectronic circuit architectures
bull Recent accomplishments include the fabrication of molecular circuits that are capable of
performing logic operations
bull So the Nanocomputer architecture is based on the QCA single electron circuit
molecular circuit ets
Quantum Dot Cellular Automata
bull For the purpose of quantum computing a molecular structural model has been proposed
that utilizes quantum dots is termed as quantum cel lular automata(QCA) in which four
quantum dots in square array are placed in a cell such that electrons are able to tunnel
between the dots but are unable to leave the cell
bull When two excess electrons are placed in the cell coulomb repulsion will force the electron
to occupy dots on opposite corners
bull Two ground states are energetically equivalent and can be labeled logic lsquo1rsquoand lsquo0rsquo
respectivelyFIGURE 1 The two possible ground-state
polarizations denoted ldquo0rdquo and ldquo1rdquo of a four-dot
QCA cell
Flipping the logic state of one cell for instance by applying a negative potential to a lead
near the quantum dot occupied by an electron will result in the next door cell flipping
ground state in order to reduce coulomb repulsion
In this way a line of QCA cells can be used to do computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 327
08-11-2013
3
bull The QCA cellular architecture is similar to other cellular arrays such as cellular
neuralnonlinear networks (CNN) in that they repeatedly employ the same basic cell with its
associated near-neighbor interconnection pattern
bull In short QCA is a proposed scheme for computing with cells of coupled quantum dots where
coupling between the cells is given by their direct physical interactions(and not by wires)
bull The physical mechanism available for interactions in such field coupled architectures are
electric (coulomb ) or magnetic interactions in conjunction with quantum mechanical tunneling
bull 11 A quantum-dot cell
bull The quantum-dot cellular automata (QCA) scheme is based on a cell which contains four quantum dots as
schematically shown in figure (a)
bull The quantum dots are represented by the open circles which indicate the confining electronic potential In
the ideal case each cell is occupied by two electrons (shown as solid dots)
bull P ri n c ip l e o f q u a n t u m d o t c el l T u n n el i n g B e t w e en d o t s amp C o u lo m b i n t er a ct i o n
between electrons
bull The two electrons experience their mutual Coulombic repulsion yet they are constrained to
occupy the quantum dots inside the cell
bull So they placed by hopping between the dots that configuration which corresponds to the
physical ground state of the cell
bull Two electrons will tend to occupy different dots on opposing corners of the cell because of
the Coulomb energy associated with having them on the same dot or bringing them together
closer
bull Figure (a) Schematic diagram of a QCA cell consisting of five
quantum dots and occupied by two electrons
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 427
08-11-2013
4
bull Polarization (P=+1 or P=-1)
bull These two configurations may be interpreted as binary information thus encoding bit
values in the electronic arrangement inside a single cell
bull The ground state of an isolated cell is a superposition with equal weight of the two basic
configurations and therefore has a net polarization of zero
Figure (b) The two basic electronic arrangements in the cell
which can be used to represent binary information P = +1 and
P = minus1
bull 12 Cell-cell coupling
bull The two polarization states of the cell will not be energetically equivalent if other cells are nearby
bull The electrons are allowed to tunnel between the dots in the same cell but not between different
cells
1 2
bull Figure shows two cells where the polarization of
cell 1 (P 1) is determined by the polarization of its
neighbor (P 2 )
bull The polarization of cell 2 is presumed to be fixed at
a given value
bull corresponding to a certain arrangement of charges
in cell 2 and this charge distribution exerts its
influence on cell 1 thus determining its polarization
P 1
bull As shown in the figure cell-1 is almost completely polarized even though cell-2 might only be
partially polarized
bull For example a polarization of P 2=01 induces almost perfect polarization in cell 1 ie P 1=099
bull In other words even a small asymmetry of charge in cell-2 is sufficient to break the degeneracy of
the two basic states in cell-1 by energetically favoring one configuration over the other
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 527
08-11-2013
5
bull 13 QCA Logic
bull Simple QCA cell logic line where a logic input of 1 gives an logic output of 1
bull This structure could be called a binary wire where a lsquo1rsquo input gives a lsquo1rsquo output
bull All of the electrons occupy positions as far away from their neighbors as possible and they
are all in ground state polarization
bull Flipping the ground state of the cell on the left end will result in a domino effect where each
neighboring cell flips ground states until the end of the wire is reached
bull Inverter Built From QCA Cells The output isrdquo0rdquo when the input is ldquo1rdquo
bull CORNER
bull Information can also flow around corners as shown in figure
bull Fan-Out
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 627
08-11-2013
6
bull Majority Gate
bull The QCA topology that can produce AND amp OR gates is called a majority gate Where three input cells ldquo
vote on the polarization of central cell ldquoThe polarization of central cell is then propagated as the output
bull One of the input can be designated a programming input and determines whether the majority gate
produces an AND or an OR If the programming gate is a logic 1 then the result is OR while
programming gate equal to logic 0 would produce a result of AND
A B C Output
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
bull In other words majority gates may be viewed as programmable AND amp OR gates and
hence the functionality of the gates may be determined by the state of computation itself
bull Computing With QCA
bull For the purpose of quantum computation QCA array can be used
bull In a QCA array cells interact with their neighbors via repulsion (ie coulomb interaction) and
no circuitry or wires are used to connect the interior cells with each other
bull This can over come the drawback of heat dissipation appears in conventional circuits
bull The information in a QCA array is contained in the physical ground state of the system
bull The two key features that characterize this new computing model are
minus Computing with the ground state
minus Edge driven computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 727
08-11-2013
7
bull Computing With The Ground State
bull Consider a QCA array before the start of a computation
bull The array left to itself will have assumed its physical ground state Presenting the input
data ie setting the polarization of the input cells will deliver energy to the system thus
promoting the array to an excited state
bull In the computation the array reaches the new ground-state configuration according to the
boundary conditions given by the fixed input cells
bull The information is contained in the ground state itself only and not in how the ground state
is reached ie the dynamics of computation
bull But the dynamics of the computation is important for the actual implementation purpose
bull There may be two approaches that can explain computationdynamics
ndash The system is completely left to itself
ndash The system is externally controlled
bull The system is completely left to itself
bull The natural tendency of the system to achieve the ground state may be used to drive the
computation process
bull The interaction of cells (with each other and also with the system) present in the surrounding of the
system try to relax the system from the excited state to the new ground state
bull The actual dynamics will be too complicated because the interactions are uncontrollable
bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed
time in which a computation is completed
bull The system is externally controlled
bull Adiabatic computing
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 2: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/2.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 227
08-11-2013
2
Introduction to Nanocomputer architecture
bull Nanotechnology holds the promise of putting a trillion molecular-scale devices in a square
centimeter How does one assemble a trillion devices per square centimeter Moreover
this needs to be done quickly inexpensively and sufficiently reliably What does one do
with a trillion devices
bull If we assume that one can make them (and they actually work) how can this massive
amount of devices be harnessed for useful computation These questions highlight the
need for innovative nanoelectronic circuit architectures
bull Recent accomplishments include the fabrication of molecular circuits that are capable of
performing logic operations
bull So the Nanocomputer architecture is based on the QCA single electron circuit
molecular circuit ets
Quantum Dot Cellular Automata
bull For the purpose of quantum computing a molecular structural model has been proposed
that utilizes quantum dots is termed as quantum cel lular automata(QCA) in which four
quantum dots in square array are placed in a cell such that electrons are able to tunnel
between the dots but are unable to leave the cell
bull When two excess electrons are placed in the cell coulomb repulsion will force the electron
to occupy dots on opposite corners
bull Two ground states are energetically equivalent and can be labeled logic lsquo1rsquoand lsquo0rsquo
respectivelyFIGURE 1 The two possible ground-state
polarizations denoted ldquo0rdquo and ldquo1rdquo of a four-dot
QCA cell
Flipping the logic state of one cell for instance by applying a negative potential to a lead
near the quantum dot occupied by an electron will result in the next door cell flipping
ground state in order to reduce coulomb repulsion
In this way a line of QCA cells can be used to do computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 327
08-11-2013
3
bull The QCA cellular architecture is similar to other cellular arrays such as cellular
neuralnonlinear networks (CNN) in that they repeatedly employ the same basic cell with its
associated near-neighbor interconnection pattern
bull In short QCA is a proposed scheme for computing with cells of coupled quantum dots where
coupling between the cells is given by their direct physical interactions(and not by wires)
bull The physical mechanism available for interactions in such field coupled architectures are
electric (coulomb ) or magnetic interactions in conjunction with quantum mechanical tunneling
bull 11 A quantum-dot cell
bull The quantum-dot cellular automata (QCA) scheme is based on a cell which contains four quantum dots as
schematically shown in figure (a)
bull The quantum dots are represented by the open circles which indicate the confining electronic potential In
the ideal case each cell is occupied by two electrons (shown as solid dots)
bull P ri n c ip l e o f q u a n t u m d o t c el l T u n n el i n g B e t w e en d o t s amp C o u lo m b i n t er a ct i o n
between electrons
bull The two electrons experience their mutual Coulombic repulsion yet they are constrained to
occupy the quantum dots inside the cell
bull So they placed by hopping between the dots that configuration which corresponds to the
physical ground state of the cell
bull Two electrons will tend to occupy different dots on opposing corners of the cell because of
the Coulomb energy associated with having them on the same dot or bringing them together
closer
bull Figure (a) Schematic diagram of a QCA cell consisting of five
quantum dots and occupied by two electrons
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 427
08-11-2013
4
bull Polarization (P=+1 or P=-1)
bull These two configurations may be interpreted as binary information thus encoding bit
values in the electronic arrangement inside a single cell
bull The ground state of an isolated cell is a superposition with equal weight of the two basic
configurations and therefore has a net polarization of zero
Figure (b) The two basic electronic arrangements in the cell
which can be used to represent binary information P = +1 and
P = minus1
bull 12 Cell-cell coupling
bull The two polarization states of the cell will not be energetically equivalent if other cells are nearby
bull The electrons are allowed to tunnel between the dots in the same cell but not between different
cells
1 2
bull Figure shows two cells where the polarization of
cell 1 (P 1) is determined by the polarization of its
neighbor (P 2 )
bull The polarization of cell 2 is presumed to be fixed at
a given value
bull corresponding to a certain arrangement of charges
in cell 2 and this charge distribution exerts its
influence on cell 1 thus determining its polarization
P 1
bull As shown in the figure cell-1 is almost completely polarized even though cell-2 might only be
partially polarized
bull For example a polarization of P 2=01 induces almost perfect polarization in cell 1 ie P 1=099
bull In other words even a small asymmetry of charge in cell-2 is sufficient to break the degeneracy of
the two basic states in cell-1 by energetically favoring one configuration over the other
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 527
08-11-2013
5
bull 13 QCA Logic
bull Simple QCA cell logic line where a logic input of 1 gives an logic output of 1
bull This structure could be called a binary wire where a lsquo1rsquo input gives a lsquo1rsquo output
bull All of the electrons occupy positions as far away from their neighbors as possible and they
are all in ground state polarization
bull Flipping the ground state of the cell on the left end will result in a domino effect where each
neighboring cell flips ground states until the end of the wire is reached
bull Inverter Built From QCA Cells The output isrdquo0rdquo when the input is ldquo1rdquo
bull CORNER
bull Information can also flow around corners as shown in figure
bull Fan-Out
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 627
08-11-2013
6
bull Majority Gate
bull The QCA topology that can produce AND amp OR gates is called a majority gate Where three input cells ldquo
vote on the polarization of central cell ldquoThe polarization of central cell is then propagated as the output
bull One of the input can be designated a programming input and determines whether the majority gate
produces an AND or an OR If the programming gate is a logic 1 then the result is OR while
programming gate equal to logic 0 would produce a result of AND
A B C Output
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
bull In other words majority gates may be viewed as programmable AND amp OR gates and
hence the functionality of the gates may be determined by the state of computation itself
bull Computing With QCA
bull For the purpose of quantum computation QCA array can be used
bull In a QCA array cells interact with their neighbors via repulsion (ie coulomb interaction) and
no circuitry or wires are used to connect the interior cells with each other
bull This can over come the drawback of heat dissipation appears in conventional circuits
bull The information in a QCA array is contained in the physical ground state of the system
bull The two key features that characterize this new computing model are
minus Computing with the ground state
minus Edge driven computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 727
08-11-2013
7
bull Computing With The Ground State
bull Consider a QCA array before the start of a computation
bull The array left to itself will have assumed its physical ground state Presenting the input
data ie setting the polarization of the input cells will deliver energy to the system thus
promoting the array to an excited state
bull In the computation the array reaches the new ground-state configuration according to the
boundary conditions given by the fixed input cells
bull The information is contained in the ground state itself only and not in how the ground state
is reached ie the dynamics of computation
bull But the dynamics of the computation is important for the actual implementation purpose
bull There may be two approaches that can explain computationdynamics
ndash The system is completely left to itself
ndash The system is externally controlled
bull The system is completely left to itself
bull The natural tendency of the system to achieve the ground state may be used to drive the
computation process
bull The interaction of cells (with each other and also with the system) present in the surrounding of the
system try to relax the system from the excited state to the new ground state
bull The actual dynamics will be too complicated because the interactions are uncontrollable
bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed
time in which a computation is completed
bull The system is externally controlled
bull Adiabatic computing
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 3: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/3.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 327
08-11-2013
3
bull The QCA cellular architecture is similar to other cellular arrays such as cellular
neuralnonlinear networks (CNN) in that they repeatedly employ the same basic cell with its
associated near-neighbor interconnection pattern
bull In short QCA is a proposed scheme for computing with cells of coupled quantum dots where
coupling between the cells is given by their direct physical interactions(and not by wires)
bull The physical mechanism available for interactions in such field coupled architectures are
electric (coulomb ) or magnetic interactions in conjunction with quantum mechanical tunneling
bull 11 A quantum-dot cell
bull The quantum-dot cellular automata (QCA) scheme is based on a cell which contains four quantum dots as
schematically shown in figure (a)
bull The quantum dots are represented by the open circles which indicate the confining electronic potential In
the ideal case each cell is occupied by two electrons (shown as solid dots)
bull P ri n c ip l e o f q u a n t u m d o t c el l T u n n el i n g B e t w e en d o t s amp C o u lo m b i n t er a ct i o n
between electrons
bull The two electrons experience their mutual Coulombic repulsion yet they are constrained to
occupy the quantum dots inside the cell
bull So they placed by hopping between the dots that configuration which corresponds to the
physical ground state of the cell
bull Two electrons will tend to occupy different dots on opposing corners of the cell because of
the Coulomb energy associated with having them on the same dot or bringing them together
closer
bull Figure (a) Schematic diagram of a QCA cell consisting of five
quantum dots and occupied by two electrons
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 427
08-11-2013
4
bull Polarization (P=+1 or P=-1)
bull These two configurations may be interpreted as binary information thus encoding bit
values in the electronic arrangement inside a single cell
bull The ground state of an isolated cell is a superposition with equal weight of the two basic
configurations and therefore has a net polarization of zero
Figure (b) The two basic electronic arrangements in the cell
which can be used to represent binary information P = +1 and
P = minus1
bull 12 Cell-cell coupling
bull The two polarization states of the cell will not be energetically equivalent if other cells are nearby
bull The electrons are allowed to tunnel between the dots in the same cell but not between different
cells
1 2
bull Figure shows two cells where the polarization of
cell 1 (P 1) is determined by the polarization of its
neighbor (P 2 )
bull The polarization of cell 2 is presumed to be fixed at
a given value
bull corresponding to a certain arrangement of charges
in cell 2 and this charge distribution exerts its
influence on cell 1 thus determining its polarization
P 1
bull As shown in the figure cell-1 is almost completely polarized even though cell-2 might only be
partially polarized
bull For example a polarization of P 2=01 induces almost perfect polarization in cell 1 ie P 1=099
bull In other words even a small asymmetry of charge in cell-2 is sufficient to break the degeneracy of
the two basic states in cell-1 by energetically favoring one configuration over the other
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 527
08-11-2013
5
bull 13 QCA Logic
bull Simple QCA cell logic line where a logic input of 1 gives an logic output of 1
bull This structure could be called a binary wire where a lsquo1rsquo input gives a lsquo1rsquo output
bull All of the electrons occupy positions as far away from their neighbors as possible and they
are all in ground state polarization
bull Flipping the ground state of the cell on the left end will result in a domino effect where each
neighboring cell flips ground states until the end of the wire is reached
bull Inverter Built From QCA Cells The output isrdquo0rdquo when the input is ldquo1rdquo
bull CORNER
bull Information can also flow around corners as shown in figure
bull Fan-Out
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 627
08-11-2013
6
bull Majority Gate
bull The QCA topology that can produce AND amp OR gates is called a majority gate Where three input cells ldquo
vote on the polarization of central cell ldquoThe polarization of central cell is then propagated as the output
bull One of the input can be designated a programming input and determines whether the majority gate
produces an AND or an OR If the programming gate is a logic 1 then the result is OR while
programming gate equal to logic 0 would produce a result of AND
A B C Output
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
bull In other words majority gates may be viewed as programmable AND amp OR gates and
hence the functionality of the gates may be determined by the state of computation itself
bull Computing With QCA
bull For the purpose of quantum computation QCA array can be used
bull In a QCA array cells interact with their neighbors via repulsion (ie coulomb interaction) and
no circuitry or wires are used to connect the interior cells with each other
bull This can over come the drawback of heat dissipation appears in conventional circuits
bull The information in a QCA array is contained in the physical ground state of the system
bull The two key features that characterize this new computing model are
minus Computing with the ground state
minus Edge driven computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 727
08-11-2013
7
bull Computing With The Ground State
bull Consider a QCA array before the start of a computation
bull The array left to itself will have assumed its physical ground state Presenting the input
data ie setting the polarization of the input cells will deliver energy to the system thus
promoting the array to an excited state
bull In the computation the array reaches the new ground-state configuration according to the
boundary conditions given by the fixed input cells
bull The information is contained in the ground state itself only and not in how the ground state
is reached ie the dynamics of computation
bull But the dynamics of the computation is important for the actual implementation purpose
bull There may be two approaches that can explain computationdynamics
ndash The system is completely left to itself
ndash The system is externally controlled
bull The system is completely left to itself
bull The natural tendency of the system to achieve the ground state may be used to drive the
computation process
bull The interaction of cells (with each other and also with the system) present in the surrounding of the
system try to relax the system from the excited state to the new ground state
bull The actual dynamics will be too complicated because the interactions are uncontrollable
bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed
time in which a computation is completed
bull The system is externally controlled
bull Adiabatic computing
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 4: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/4.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 427
08-11-2013
4
bull Polarization (P=+1 or P=-1)
bull These two configurations may be interpreted as binary information thus encoding bit
values in the electronic arrangement inside a single cell
bull The ground state of an isolated cell is a superposition with equal weight of the two basic
configurations and therefore has a net polarization of zero
Figure (b) The two basic electronic arrangements in the cell
which can be used to represent binary information P = +1 and
P = minus1
bull 12 Cell-cell coupling
bull The two polarization states of the cell will not be energetically equivalent if other cells are nearby
bull The electrons are allowed to tunnel between the dots in the same cell but not between different
cells
1 2
bull Figure shows two cells where the polarization of
cell 1 (P 1) is determined by the polarization of its
neighbor (P 2 )
bull The polarization of cell 2 is presumed to be fixed at
a given value
bull corresponding to a certain arrangement of charges
in cell 2 and this charge distribution exerts its
influence on cell 1 thus determining its polarization
P 1
bull As shown in the figure cell-1 is almost completely polarized even though cell-2 might only be
partially polarized
bull For example a polarization of P 2=01 induces almost perfect polarization in cell 1 ie P 1=099
bull In other words even a small asymmetry of charge in cell-2 is sufficient to break the degeneracy of
the two basic states in cell-1 by energetically favoring one configuration over the other
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 527
08-11-2013
5
bull 13 QCA Logic
bull Simple QCA cell logic line where a logic input of 1 gives an logic output of 1
bull This structure could be called a binary wire where a lsquo1rsquo input gives a lsquo1rsquo output
bull All of the electrons occupy positions as far away from their neighbors as possible and they
are all in ground state polarization
bull Flipping the ground state of the cell on the left end will result in a domino effect where each
neighboring cell flips ground states until the end of the wire is reached
bull Inverter Built From QCA Cells The output isrdquo0rdquo when the input is ldquo1rdquo
bull CORNER
bull Information can also flow around corners as shown in figure
bull Fan-Out
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 627
08-11-2013
6
bull Majority Gate
bull The QCA topology that can produce AND amp OR gates is called a majority gate Where three input cells ldquo
vote on the polarization of central cell ldquoThe polarization of central cell is then propagated as the output
bull One of the input can be designated a programming input and determines whether the majority gate
produces an AND or an OR If the programming gate is a logic 1 then the result is OR while
programming gate equal to logic 0 would produce a result of AND
A B C Output
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
bull In other words majority gates may be viewed as programmable AND amp OR gates and
hence the functionality of the gates may be determined by the state of computation itself
bull Computing With QCA
bull For the purpose of quantum computation QCA array can be used
bull In a QCA array cells interact with their neighbors via repulsion (ie coulomb interaction) and
no circuitry or wires are used to connect the interior cells with each other
bull This can over come the drawback of heat dissipation appears in conventional circuits
bull The information in a QCA array is contained in the physical ground state of the system
bull The two key features that characterize this new computing model are
minus Computing with the ground state
minus Edge driven computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 727
08-11-2013
7
bull Computing With The Ground State
bull Consider a QCA array before the start of a computation
bull The array left to itself will have assumed its physical ground state Presenting the input
data ie setting the polarization of the input cells will deliver energy to the system thus
promoting the array to an excited state
bull In the computation the array reaches the new ground-state configuration according to the
boundary conditions given by the fixed input cells
bull The information is contained in the ground state itself only and not in how the ground state
is reached ie the dynamics of computation
bull But the dynamics of the computation is important for the actual implementation purpose
bull There may be two approaches that can explain computationdynamics
ndash The system is completely left to itself
ndash The system is externally controlled
bull The system is completely left to itself
bull The natural tendency of the system to achieve the ground state may be used to drive the
computation process
bull The interaction of cells (with each other and also with the system) present in the surrounding of the
system try to relax the system from the excited state to the new ground state
bull The actual dynamics will be too complicated because the interactions are uncontrollable
bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed
time in which a computation is completed
bull The system is externally controlled
bull Adiabatic computing
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 5: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/5.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 527
08-11-2013
5
bull 13 QCA Logic
bull Simple QCA cell logic line where a logic input of 1 gives an logic output of 1
bull This structure could be called a binary wire where a lsquo1rsquo input gives a lsquo1rsquo output
bull All of the electrons occupy positions as far away from their neighbors as possible and they
are all in ground state polarization
bull Flipping the ground state of the cell on the left end will result in a domino effect where each
neighboring cell flips ground states until the end of the wire is reached
bull Inverter Built From QCA Cells The output isrdquo0rdquo when the input is ldquo1rdquo
bull CORNER
bull Information can also flow around corners as shown in figure
bull Fan-Out
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 627
08-11-2013
6
bull Majority Gate
bull The QCA topology that can produce AND amp OR gates is called a majority gate Where three input cells ldquo
vote on the polarization of central cell ldquoThe polarization of central cell is then propagated as the output
bull One of the input can be designated a programming input and determines whether the majority gate
produces an AND or an OR If the programming gate is a logic 1 then the result is OR while
programming gate equal to logic 0 would produce a result of AND
A B C Output
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
bull In other words majority gates may be viewed as programmable AND amp OR gates and
hence the functionality of the gates may be determined by the state of computation itself
bull Computing With QCA
bull For the purpose of quantum computation QCA array can be used
bull In a QCA array cells interact with their neighbors via repulsion (ie coulomb interaction) and
no circuitry or wires are used to connect the interior cells with each other
bull This can over come the drawback of heat dissipation appears in conventional circuits
bull The information in a QCA array is contained in the physical ground state of the system
bull The two key features that characterize this new computing model are
minus Computing with the ground state
minus Edge driven computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 727
08-11-2013
7
bull Computing With The Ground State
bull Consider a QCA array before the start of a computation
bull The array left to itself will have assumed its physical ground state Presenting the input
data ie setting the polarization of the input cells will deliver energy to the system thus
promoting the array to an excited state
bull In the computation the array reaches the new ground-state configuration according to the
boundary conditions given by the fixed input cells
bull The information is contained in the ground state itself only and not in how the ground state
is reached ie the dynamics of computation
bull But the dynamics of the computation is important for the actual implementation purpose
bull There may be two approaches that can explain computationdynamics
ndash The system is completely left to itself
ndash The system is externally controlled
bull The system is completely left to itself
bull The natural tendency of the system to achieve the ground state may be used to drive the
computation process
bull The interaction of cells (with each other and also with the system) present in the surrounding of the
system try to relax the system from the excited state to the new ground state
bull The actual dynamics will be too complicated because the interactions are uncontrollable
bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed
time in which a computation is completed
bull The system is externally controlled
bull Adiabatic computing
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 6: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/6.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 627
08-11-2013
6
bull Majority Gate
bull The QCA topology that can produce AND amp OR gates is called a majority gate Where three input cells ldquo
vote on the polarization of central cell ldquoThe polarization of central cell is then propagated as the output
bull One of the input can be designated a programming input and determines whether the majority gate
produces an AND or an OR If the programming gate is a logic 1 then the result is OR while
programming gate equal to logic 0 would produce a result of AND
A B C Output
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
bull In other words majority gates may be viewed as programmable AND amp OR gates and
hence the functionality of the gates may be determined by the state of computation itself
bull Computing With QCA
bull For the purpose of quantum computation QCA array can be used
bull In a QCA array cells interact with their neighbors via repulsion (ie coulomb interaction) and
no circuitry or wires are used to connect the interior cells with each other
bull This can over come the drawback of heat dissipation appears in conventional circuits
bull The information in a QCA array is contained in the physical ground state of the system
bull The two key features that characterize this new computing model are
minus Computing with the ground state
minus Edge driven computation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 727
08-11-2013
7
bull Computing With The Ground State
bull Consider a QCA array before the start of a computation
bull The array left to itself will have assumed its physical ground state Presenting the input
data ie setting the polarization of the input cells will deliver energy to the system thus
promoting the array to an excited state
bull In the computation the array reaches the new ground-state configuration according to the
boundary conditions given by the fixed input cells
bull The information is contained in the ground state itself only and not in how the ground state
is reached ie the dynamics of computation
bull But the dynamics of the computation is important for the actual implementation purpose
bull There may be two approaches that can explain computationdynamics
ndash The system is completely left to itself
ndash The system is externally controlled
bull The system is completely left to itself
bull The natural tendency of the system to achieve the ground state may be used to drive the
computation process
bull The interaction of cells (with each other and also with the system) present in the surrounding of the
system try to relax the system from the excited state to the new ground state
bull The actual dynamics will be too complicated because the interactions are uncontrollable
bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed
time in which a computation is completed
bull The system is externally controlled
bull Adiabatic computing
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 7: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/7.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 727
08-11-2013
7
bull Computing With The Ground State
bull Consider a QCA array before the start of a computation
bull The array left to itself will have assumed its physical ground state Presenting the input
data ie setting the polarization of the input cells will deliver energy to the system thus
promoting the array to an excited state
bull In the computation the array reaches the new ground-state configuration according to the
boundary conditions given by the fixed input cells
bull The information is contained in the ground state itself only and not in how the ground state
is reached ie the dynamics of computation
bull But the dynamics of the computation is important for the actual implementation purpose
bull There may be two approaches that can explain computationdynamics
ndash The system is completely left to itself
ndash The system is externally controlled
bull The system is completely left to itself
bull The natural tendency of the system to achieve the ground state may be used to drive the
computation process
bull The interaction of cells (with each other and also with the system) present in the surrounding of the
system try to relax the system from the excited state to the new ground state
bull The actual dynamics will be too complicated because the interactions are uncontrollable
bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed
time in which a computation is completed
bull The system is externally controlled
bull Adiabatic computing
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock
signals
bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis
pipeline architectureshave been proposed
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 8: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/8.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 827
08-11-2013
8
bull EDGE DRIVEN COMPUTATION
bull Edge-driven computation means that only the periphery of a QCA array can be contacted
which is used to write the input data and to read the output of the computation No internal
cells may be contacted directly
bull This implies that no signals or power can be delivered from the outside to the interior of an
array All interior cells only interact within their local neighborhood The absence of signal and
power lines to each and every interior cell has obvious benefits for the interconnect problem
and the heat dissipation
bull The lack of direct contact to the interior cells also has profound consequences for the way
such arrays can be used for computation Because no power can flow from the outside
interior cells cannot be maintained in a far-from-equilibrium state Because no external signals
are brought to the inside internal cells cannot be influenced directly
bull These are the reasons why the ground state of the whole array is used to represent the
information as opposed to the states of each individual cell In fact edge-driven computation
necessitates computing with the ground state
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 9: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/9.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 927
08-11-2013
9
Single Electron Circuit
bull A single electron circuit (SEC) consists of electronic devices (like transistor
diodes etc) whose working is based on the State change of device due to
presence or absence of a single electron
bull Single electron transistors (SETs) can be used (in principle) in circuit to the
conventional silicon FETs MOSFETs
bull But there are practical problem in using SETs as logic devices in conventional
circuit architectures
bull One of the main problem related to the presence of charges in the surrounding
circuitry which change the SET characteristics in an uncontrollable way because
the SET is sensitive to the charge of one electron So Solution of above
problem is the whole surrounding circuitry must be of same nature ie it must
use all single electron devices
bull Design As schematically shown in Figure the basic building block for SEC logic family consists
of three conducting islands where the middle island is slightly shifted off the line passing through
the centres of the edge island
bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not
directly between the edge islands (due to their larger spatial separation)
bull Let us assume that each cell can be occupied by one additional
electron and that a clock electric field is applied that initially
pushes this electron onto the middle island (the direction of this
clock field is perpendicular to the line connecting the edge
islands)
bull Now that the electron is located on the central island the clock field is reduced and the electron
eventually changes direction At some point in time during this cycle it will be energetically
favourable for the electron to tunnel- off of the middle island and onto one of the edge islands
bull If both islands are identical the choice of island will be random However this symmetry can be
broken by a small switching field that is applied perpendicular to the clock field and along the line
of the edge cells This control over the leftndashright final position of the electron can be interpreted as
one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left
island logical ldquo0rdquo
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 10: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/10.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1027
08-11-2013
10
Molecular Circuit
bull Chemical self-assembly processes look promising since they (in principle) allow vast
amounts of devices to be fabricated very cheaply
bull But there are key problems
(1) the need to create complex circuits for computers appears to be ill suited for chemical
self-assembly which yields mostly regular (periodic) structures and
(2) the need to deal with very large numbers of components and to arrange them into useful
structures is a hard problem (NP-hard problem)
bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the
molecular scale
bull There are some approach to built molecular circuit
bull First
bull One approach to molecular electronics is to build circuits in analogy to conventional
silicon-based electronics The idea is to find molecular analogs of electronic devices
(such as wires diodes transistors etc) and then to assemble these into molecular
circuits
bull Second
bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)
concept of an atom relay which was proposed by Wada and coworkers
bull The atom relay is a switching device based upon the controlled motion of a single atom
bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching
atom and a switching gate
bull The operation principle of the atom relay is that the switching atom is displaced from the atom
wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)
bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay
configuration have been proposed and their operation was examined through simulation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 11: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/11.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1127
08-11-2013
11
bull Transistor
bull A popular group of molecules that can work as the semiconducting channel material in a
molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb
blockade mechanism when placed between the source and drain electrode in an appropriate
way Fullerenes work by the same mechanism and have also been commonly utilized
bull Wires
bull The sole purpose of molecular wires is to electrically connect different parts of a molecular
electrical circuit As the assembly of these and their connection to a macroscopic circuit is still
not mastered the focus of research in single molecule electronics is primarily on the
functionalized molecules molecular wires are characterized by containing no functional
groups and are hence composed of plain repetitions of a conjugated building block Among
these are the carbon nanotubes that are quite large compared to the other suggestions but
have shown very promising electrical properties
Bra-ket Notation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 12: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/12.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1227
08-11-2013
12
Quantum superposition
bull The superposition principle plays the most important role in all consideration of quantum
information and in most experiments of quantum mechanics
bull Double slit experiment
bull The essential ingredients of double slit experiment are a source a double slit assembly and an
observation screen on which we observe interference fringes According to
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 13: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/13.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1327
08-11-2013
13
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 14: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/14.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1427
08-11-2013
14
Q-bitsbull QUBIT
bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer
same as bit which is the basic unit of information in classical computer
bull In a quantum computer a number of elemental particles such as electrons or photons can
be used with either their charge or polarization acting as a representation of 0 andor 1
bull Each of these particles is known as a qubit the nature and behavior of these particles (as
expressed in quantum theory) form the basis of quantum computing
bull Bit Vs Qbit
bull A bit is the basic unit of computer information Regardless of its physical realization a bit is
always understood to be either a 0 or a 1
bull An analogy to this is a light switch- with the off position representing 0 and the on position
representing 1
bull A qubit has some similarities to a classical bit but is overall very different
bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that
whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both
bull Quantum superposition refers to the quantum
mechanical property of a particle to occupy all of its
possible quantum states simultaneously
bull Due to this property to completely describe a particle
one must include a description of every possible state
and the probability of the particle being in that state
bull In above figure second row shown the qbit representation of decimal 5 Third row shows the
qbit may represent superposition of decimal 4 and decimal 5
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 15: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/15.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1527
08-11-2013
15
bull Since the Schroumldinger equation is linear a solution that takes into account all possible
states will be a Linear combination of the solutions for each individual state This
mathematical property of linear equations is known as the superposition principle
bull Representation of qbit
bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to
represent them This means that the two computational basis states are conventionally
written as and (pronounced ket 0 and ket 1)
bull Qbit states
bull A pure qubit state is a linear superposition of those two states This means that the qubit
can be represented as a linear combination of |0gt and |1gt
bull where α and β are probability amplitudes and can in general both be complex numbers
bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2
and the probability of outcome |1gt is | β |2
bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and
β must be represented by the equation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 16: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/16.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1627
08-11-2013
16
Rough
bull state space of a single qubit register can be represented geometrically by the Bloch
sphere
bull The possible states for a single qubit can be visualised using a
Bloch sphere (see diagram)
bull Represented on such a sphere a classical bit could only be at the
North Pole or the South Pole in the locations where and are
respectively
bull The rest of the surface of the sphere is inaccessible to a classical
bit but a pure qubit state can be represented by any point on the
surface
bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis
bull The surface of the sphere is two-dimensional space which
represents the state space of the pure qubit statesbull This state space has two local degrees of freedom
bull It might at first sight seem that there should be four degrees of
freedom as α and β are complex numbers with two degrees of
freedom each However one degree of freedom is removed by the
constraint
bull Another the overall phase of the state has no physically observable
consequences so we can arbitrarily choose α to be real leaving just
two degrees of freedom
bull It is possible to put the qubit in a mixed state a statistical
combination of different pure states Mixed states can be
represented by points inside the Bloch sphere
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 17: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/17.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1727
08-11-2013
17
bull Kind of operations
bull There are various kinds of physical operations that can be performed on pure qubit
states
bull Unitary transformation These correspond to rotations of the Bloch sphere
bull Standard basis measurement It is an operation in which information is gained
about the state of the qubit With probability | α |2 the result of the measurement will
be and with probability | β |2 it will be Measurement of the state of the qubit
alters the values of α and β For instance if the state is measured α is changed to
1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state
entangled with another quantum system transforms a pure state into a mixed state
Physical representation
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 18: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/18.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1827
08-11-2013
18
Single qbit transformation (Quantum GATE)Beam splitter
The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 19: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/19.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 1927
08-11-2013
19
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 20: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/20.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2027
08-11-2013
20
Phase Shifter
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 21: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/21.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2127
08-11-2013
21
Quantum GATE
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 22: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/22.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2227
08-11-2013
22
Controlled GATE
ndash So we have discussed only single qbit gates that is which involve one bit only
ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one
bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum
controlled NOT gate
ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second
qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the
matrix
ndash The action of quantum controlled NOT gate can be described by
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 23: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/23.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2327
08-11-2013
23
bull Controlled Not GATE can be represented by matrix
bull Controlled U GATE
bull if U is a gate that operates on single qubits with matrix representation
QUANTUM CIRCUIT MODEL
bull In quantum information theory a quantum circuit is a model for quantum computation in
which a computation is a sequence of quantum gates And This structure is referred to
as an n-qubit register
bull Proposed Models of quantum computation
1 Quantum Dot Cellular Automata
2 Quantum Gate Array
3 Quantum Turing Machine
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 24: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/24.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2427
08-11-2013
24
bull Quantum gate array
bull Important feature of computer is that they can be programmable so in case of programmable
quantum computer device would have to have the features that
bull It should consist of a fixed gate array with a data register and program register
bull And the array should work in such a way that the state of the program register
emcodes the unitary operator u that is applied to the state of data register
bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and
program register together with a final fixed projective measurement on the composite
systemrdquo
bull Suppose that we are given a quantum system prepared in the same state q and an operator
O by specifying its expansion in a basis of the space of operators so our task is to compute
the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable
circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo
Inputs of such circuits are data register program register and auxiliary qubit
bull QUANTUM TURING MACHINE
bull Turing machine is an idea of computing machine which moved from one state to another using a precise
finite set of rules given by finite table and depending on a single symbol it read from a tape
bull First turing machine which was a hypothetical computer consist of the following
ndash An infinite tape on which symbol may be read or written
ndash The machine travels right or left along the tape following a program
ndash At each step the machine writes to the tape travels either left or right and changes states according
to a set of internal states
ndash The set of symbols and set of internal states are both finite states
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 25: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/25.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2527
08-11-2013
25
Application of quantum mechanical system
bull Quantum CRYPTOGRAPHY
bull Cryptography is the method of hiding the secrate information It is the greek word which means
ldquohidden secraterdquo There are two main tasks of cryptography
bull Encryption
bull Decryption
bull Encryption is the method of converting information from a readable state to nonsense while
decryption is the method of converting the nonsense to the readable state
bull The user retain the ability to decrypt the data or information by the key which is generated at
the time of encryption and therefore by the use of encryption the user can avoid unwanted
person being able to read it
bull The quantum cryptography describes the use of quantum mechanical effects like quantum
communication and quantum computing to perform cryptographic task or to break
cryptographic systems
bull The well known example of quantum cryptography are the use of quantum communication to
secure exchange the key which is known as quantum key distribution and the use of quantum
computes that would allow the breaking of various popular public-key encryption
bull Quantum mechanical computations for simulation
bull The Quantum Mechanical computation systems can also be used on a very large scale
molecular systems to reduce the noise using self consistent field method where self consistent
field method is the method which is used in simulation of molecules to minimize the energy so
that the noise can be minimized
bull In a large molecular system we cannot perform the simulation or computing task because the
energy value of the large molecules is high and therefore with high energy value the large
quantity of noise is also present in the system
bull PROPAGATOR
bull In quantum mechanics and quantum field theory the propagator gives the probability
amplitude for a particle to travel from one place to another in a given time or to travel with a
certain energy and momentum
bull Propagators are used to represent the contribution of virtual particles on the internal lines of
Feynman diagrams
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 26: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/26.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2627
08-11-2013
26
bull Let us take an example for quantum mechanical system application propagate and
cryptography
bull Suppose there are two users John and Mick and John wants to send the secrete information
to Mick then John will first encrypt the data from readable state to nonsense by using a key
which is send via a quantum communication route to Mick
bull This quantum communication route is known as propagator
bull After that the John send the nonsense through any chipper media to Mick
bull After receiving the nonsense Mick will decrypt the information with the help of that key
Superdense coding
bull Suppose Alice wishes to send Bob two classical bits of information
bull Superdense coding is a way of achieving this task over a quantum channel requiring only
that Alice send one qubit to Bob
bull Alice and Bob must initially share the Bell state
bull Suppose Alice is in possession of the first qubit and Bob the second qubit
bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to
communicate to Bob
bull For convenience we remind you again of the definitions of the Pauli gates
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51
![Page 27: Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf](https://reader031.vdocuments.site/reader031/viewer/2022021318/577cd6751a28ab9e789c6e44/html5/thumbnails/27.jpg)
8142019 Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCTpdf
httpslidepdfcomreaderfullnanoelectronics-and-nanophotonicsmnt-301-unit-3ggctpdf 2727
08-11-2013
bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently
applies the identity gate I )
bull If she wishes to send 01 she applies the X gate to her qubit
bull If she wishes to send 10 she applies the Z gate
bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z
gate)
bull The following list summarizes the resulting joint 2-qubit state in each case
bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so
allows him to determine with certainty the two classical bits Alice wanted to communicate to
him The superdense coding protocol is il lustrated in Figure 51