quantum computer

• Quantum Computer

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Quantum computer

1 A Quantum Computer with spins as quantum bits was also formulated for

use as a quantum space-time in 1969.


Quantum computer

1 Although Quantum Computing is still in its infancy, experiments have been carried out in which Quantum Computational operations

were executed on a very small number of qubits (quantum bits). Both practical and theoretical research continues, and many national governments and military funding

agencies support Quantum Computing research to develop Quantum Computers for both civilian and national security purposes,

such as cryptanalysis.


Quantum computer

1 Large-scale Quantum Computers will be able to solve certain problems

much more quickly than any classical computer using the best currently

known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-

body systems


Quantum computer - Basis

1 A quantum computer operates by setting the qubits in a controlled initial state that represents the

problem at hand and by manipulating those qubits with a fixed sequence of quantum logic

gates


Quantum computer - Basis

1 An example of an implementation of qubits for a quantum computer could start with the use of particles with two spin states: "down" and "up" (typically written and , or and ). But in fact any

system possessing an observable quantity A, which is conserved under time evolution such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable

candidate for implementing a qubit. This is true because any such system can be mapped onto

an effective spin-1/2 system.


Quantum computer - Bits vs. qubits

1 A Quantum Computer with a given number of qubits is fundamentally different from a classical computer composed of the same number of

classical bits


Quantum computer - Bits vs. qubits

1 The state of a three-qubit Quantum Computer is similarly described by

an eight-dimensional vector (a,b,c,d,e,f,g,h), called a ket


Quantum computer - Operation

1 However, by repeatedly initializing, running and measuring the quantum computer, the probability of getting

the correct answer can be increased.


Quantum computer - Operation

1 For more details on the sequences of operations used for various quantum algorithms, see universal quantum

computer, Shor's algorithm, Grover's algorithm, Deutsch-Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and

quantum error correction.


Quantum computer - Potential

1 This ability would allow a Quantum Computer to decrypt many of the

cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for

solving the problem



1 Lattice-based cryptosystems are also not known to be broken by Quantum Computers, and finding a polynomial

time algorithm for solving the dihedral hidden subgroup problem,

which would break many lattice based cryptosystems, is a well-

studied open problem



1 For some problems, Quantum

Computers offer a polynomial speedup



1 For problems with all four properties, the time for a Quantum Computer to solve this will be proportional to the square root of the number of inputs. That can be a very large speedup,

reducing some problems from years to seconds. It can be used to attack

symmetric ciphers such as Triple DES and AES by attempting to guess the

secret key.https://store.theartofservice.com/the-quantum-computer-toolkit.html


1 There are a number of technical challenges in building a large-scale Quantum Computer, and thus far Quantum Computers have yet to

solve a problem faster than a classical computer. David

DiVincenzo, of IBM, listed the following requirements for a practical

Quantum Computer:


Quantum computer - Quantum decoherence

1 A very different approach to the stability-decoherence problem is to

create a topological Quantum Computer with anyons, quasi-

particles used as threads and relying on braid theory to form stable logic

gates.


Quantum computer - Developments

1 One-way Quantum Computer (computation decomposed into

sequence of one-qubit measurements applied to a highly entangled initial state or cluster

state)



1 Adiabatic Quantum Computer or computer based on Quantum

annealing (computation decomposed into a slow continuous

transformation of an initial Hamiltonian into a final Hamiltonian,

whose ground states contains the solution)



1 Topological Quantum Computer (computation decomposed into the braiding of anyons in a

2D lattice)



1 For physically implementing a Quantum Computer, many different

candidates are being pursued, among them (distinguished by the physical system used to realize the

qubits):



1 Superconductor-based Quantum Computers (including SQUID-based

Quantum Computers) (qubit implemented by the state of small

superconducting circuits (Josephson junctions))



1 Trapped ion Quantum Computer (qubit implemented by the internal state of trapped

ions)



1 Electrically defined or self-assembled quantum dots (e.g. the Loss-

DiVincenzo Quantum Computer or) (qubit given by the spin states of an electron trapped in the quantum dot)



1 Quantum dot charge based semiconductor Quantum Computer (qubit is the position of an electron

inside a double quantum dot)



1 Solid-state NMR Kane Quantum Computers (qubit realized by the nuclear spin state of phosphorus

donors in silicon)



1 Electrons-on-helium Quantum Computers (qubit is the electron

spin)



1 Fullerene-based ESR Quantum Computer (qubit based on the

electronic spin of atoms or molecules encased in fullerene structures)



1 Optics-based Quantum Computer (Quantum optics) (qubits realized by appropriate states of different modes

of the electromagnetic field, e.g.)



1 Diamond-based Quantum Computer (qubit realized by the electronic or nuclear spin of Nitrogen-vacancy

centers in diamond)



1 Bose–Einstein condensate-based Quantum Computer



1 Transistor-based Quantum Computer – string Quantum Computers with

entrainment of positive holes using an electrostatic trap



1 Rare-earth-metal-ion-doped inorganic crystal based Quantum Computers

(qubit realized by the internal electronic state of dopants in optical

fibers)



1 This approach was liked by investors more than by some academic critics,

who said that D-Wave had not yet sufficiently demonstrated that they

really had a Quantum Computer



1 In September 2011 researchers also proved that a Quantum Computer can be made with a Von Neumann architecture (separation of RAM).



1 In April 2012 a multinational team of researchers from the University of

Southern California, Delft University of Technology, the Iowa State

University of Science and Technology, and the University of

California, Santa Barbara, constructed a two-qubit Quantum Computer on a crystal of diamond

doped with some manner of impurity, that can easily be scaled up in size

and functionality at room temperature



1 In September 2012, Australian researchers at the University of New

South Wales said the world's first Quantum Computer was just 5 to 10

years away, after announcing a global breakthrough enabling

manufacture of its memory building blocks. A research team led by

Australian engineers created the first working "quantum bit" based on a single atom in silicon, invoking the same technological platform that

forms the building blocks of modern day computers, laptops and phones.



1 In February 2013, a new technique Boson Sampling was reported by two

groups using photons in an optical lattice that is not a universal

Quantum Computer but which may be good enough for practical

problems. Science Feb 15, 2013



1 In May 2013, Google Inc announced that it was launching the Quantum

Artificial Intelligence Lab, to be hosted by NASA’s Ames Research Center. The lab will house a 512-qubit Quantum Computer from D-

Wave Systems, and the USRA (Universities Space Research

Association) will invite researchers from around the world to share time on it. The goal being to study how

Quantum Computing might advance machine learning


Quantum computer - Relation to computational complexity theory

1 A quantum computer is said to "solve" a problem if, for every

instance, its answer will be right with high probability



1 BQP is suspected to be disjoint from NP-complete and a strict superset of P, but that is not known. Both integer factorization and discrete log are in BQP. Both of these problems are NP problems suspected to be outside BPP, and hence outside P. Both are suspected to not be NP-complete. There is a common misconception that quantum computers can solve

NP-complete problems in polynomial time. That is not known to be true, and is generally suspected to be

false.



1 The capacity of a quantum computer to accelerate classical algorithms has

rigid limits—upper bounds of quantum computation's complexity. The overwhelming part of classical calculations cannot be accelerated on a quantum computer. A similar

fact takes place for particular computational tasks, like the search

problem, for which Grover's algorithm is optimal.



1 The existence of "standard" quantum computers does not disprove the Church–

Turing thesis


Adiabatic quantum computation - D-Wave Quantum Computers

1 The D-Wave is an adiabatic quantum computer made by a Canadian company of the same name.

Lockheed-Martin purchased one for $10 million in 2011 and Google

purchased a Model 2 D-Wave in May 2013 with 512 qubits.


Nuclear magnetic resonance quantum computer

1 NMR Quantum Computing uses the spin states of molecules as qubits.

NMR differs from other implementations of Quantum Computers in that it uses an

ensemble of systems, in this case molecules. The ensemble is initialized to be the thermal

equilibrium state (see quantum statistical mechanics). In

mathematical parlance, this state is given by the density matrix:



1 Some early success was obtained in performing quantum algorithms in NMR systems due to the relative maturity of NMR technology. For

instance, in 2001 researchers at IBM reported the successful

implementation of Shor's algorithm in a 7-qubit NMR Quantum Computer.



1 Hence NMR Quantum Computing experiments are likely to have been

only classical simulations of a Quantum Computer.


One-way quantum computer

1 The one-way or measurement based Quantum Computer is a method of

Quantum Computing that first prepares an entangled resource

state, usually a cluster state or graph state, then performs single qubit

measurements on it. It is "one-way" because the resource state is

destroyed by the measurements.


One-way quantum computer - Implementations

1 One-way quantum computation has been demonstrated by running the 2

qubit Grover's algorithm on a 2x2 cluster state of photons. A linear

optics quantum computer based on one-way computation has been

proposed.


Kane quantum computer

1 The Kane Quantum Computer is a proposal for a scalable Quantum

Computer proposed by Bruce Kane in 1998, then at the University of New South Wales. Often thought of as a hybrid between quantum dot and

NMR Quantum Computers, the Kane computer is based on an array of

individual phosphorus donor atoms embedded in a pure silicon lattice.

Both the nuclear spins of the donors and the spins of the donor electrons

participate in the computation.



1 Nuclear spin is useful to perform single-qubit operations, but to make

a Quantum Computer, two-qubit operations are also required



1 Unlike many Quantum Computation schemes, the Kane Quantum

Computer is in principle scalable to an arbitrary number of qubits. This is

possible because qubits may be individually addressed by electrical

means.



1 The group remains optimistic that a practical large-scale Quantum Computer can be built.


Non-deterministic Turing machine - Comparison with quantum computers

1 It is a common misconception that quantum computers are NTMs. It is believed but has not been proven

that the power of quantum computers is incomparable to that of NTMs. That is, problems likely exist that an NTM could efficiently solve

that a quantum computer cannot. A likely example of problems solvable

by NTMs but not by quantum computers in polynomial time are NP-

complete problems.


Trapped ion quantum computer

1 A trapped ion Quantum Computer is a type of Quantum

Computer


Trapped ion quantum computer

1 This makes the trapped ion Quantum Computer system one of the most

promising architectures for a scalable, universal Quantum

Computer


Topological quantum computer

1 To live up to its name, a topological Quantum Computer must provide the

unique computation properties promised by a conventional Quantum

Computer design, which uses trapped quantum particles.

Fortunately in 2002, Michael H. Freedman along with Zhenghan Wang, both with Microsoft, and

Michael Larsen of Indiana University proved that a topological Quantum Computer can, in principle, perform

any computation that a conventional Quantum Computer can do.


Topological quantum computer

1 However, any level of precision for the answer can be obtained by adding more braid twists (logic

circuits) to the topological Quantum Computer, in a simple linear

relationship


Loss-DiVincenzo quantum computer

1 This was done in a way that fulfilled DiVincenzo Criteria for a scalable Quantum

Computer,D


Loss-DiVincenzo quantum computer

1 A candidate for such a Quantum Computer is a

lateral quantum dot system.


Loss-DiVincenzo quantum computer - Implementation of the two-qubit gate

1 The Loss–DiVincenzo quantum computer operates, basically, using

inter-dot gate voltage for implementing Swap (computer science) operations and local

magnetic fields (or any other local spin manipulation) for implementing

the Controlled NOT gate (CNOT gate).


Diamond-based quantum computer

1 An individual N-V center can be viewed as a basic unit of a Quantum

Computer, and it has potential applications in novel, more efficient

fields of electronics and computational science including

quantum cryptography and spintronics.


Diamond-based quantum computer - Energy level structure and its manipulation by external fields

1 The first pulse coherently excites the electron spins, and this coherence is then manipulated and probed by the subsequent pulses. Those dynamic

effects are rather important for practical realization of quantum

computers, which ought to work at high frequency.


Nanoelectronics - Quantum computers

1 Entirely new approaches for computing exploit the laws of quantum mechanics for novel

quantum computers, which enable the use of fast quantum algorithms. The Quantum computer has quantum bit memory space termed Qubit for several computations at the same time. This facility may improve the performance of the older systems.


Quantum computers

1 A quantum computer with spins as quantum bits was also formulated for

use as a quantum space–time in 1969.


Quantum computers

1 quantum computing is still in its infancy but experiments have been

carried out in which quantum computational operations were

executed on a very small number of qubits (quantum

bits).[http://phys.org/news/2013-01-qubit-bodes-future-quantum.html New qubit control bodes well for

future of quantum computing] Both practical and theoretical research

continues, and many national governments and military funding

agencies support quantum computing research to develop

quantum computers for both civilian and national security purposes, such

as cryptanalysis.[http://qist.lanl.gov/qcomp_map.shtml Quantum Information Science and Technology Roadmap] for a sense of where the research is

heading.


Quantum computers

1 Large-scale quantum computers will be able to solve certain problems

much more quickly than any classical computer using the best currently

known algorithms, like integer factorization using Shor's algorithm

or the Quantum algorithm#Quantum simulation|simulation of quantum

many-body systems


Search algorithm - For quantum computers

1 There are also search methods designed for quantum computers, like Grover's algorithm, that are theoretically faster than linear or

brute-force search even without the help of data structures or heuristics.


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