kevin resch iqc, dept. of physics university of waterloo
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Kevin ReschKevin Resch
IQC, Dept. of PhysicsIQC, Dept. of Physics
University of WaterlooUniversity of Waterloo
Quantum information:Quantum information: from the optics laboratory to the “real” worldfrom the optics laboratory to the “real” world
Institute for Quantum Institute for Quantum ComputingComputing
Waterloo, Ontario
http://www.iqc.ca/
14 faculty14 faculty
6 post-docs6 post-docs
~50 students~50 students
Always looking for more!Always looking for more!
Founded 2001 at Founded 2001 at University of University of WaterlooWaterloo
Optical quantum Optical quantum informationinformation
QuantumInformation
Quantum Computation
Quantum Communication
Quantum Metrology
QuantumFoundations
Nonlinear Optics
Measurement-Measurement-induced induced nonlinearitynonlinearity
Interference-Interference-enhanced enhanced nonlinearitynonlinearity
One-way One-way quantum quantum computationcomputation
Linear optics Linear optics entangling gatesentangling gates
Free-space Free-space entanglement entanglement distributiondistribution
Entanglement Entanglement PurificationPurification
Classical Classical analogues of analogues of quantum quantum interferenceinterference
TomographyTomography
Weak Weak measuremenmeasurementt
Multipartite Multipartite entanglemenentanglementt
Nonlocality Nonlocality teststests
Talk OutlineTalk Outline
Quantum informationQuantum informationQuantum bits can be 0 or 1 but also superpositions
bit: 0 or 1qubit: |0 + |1
|0
|1
Atomic Levels|0 = |H
|1 = |V
Photon Polarization
Familiar quantum featuresFamiliar quantum features
Uncertainty principleUncertainty principle
W. Heisenberg
2
px
Position Momentum
No-cloning theoremNo-cloning theorem
ZurekWoottersDieks
NOPE0
……leads to ultimate leads to ultimate cryptosystemcryptosystem
C. Bennett, G. Brassard 1984
Single photons Single photons are sent in one are sent in one of two of two noncommuting noncommuting basis statesbasis states
“X” “P”
An An eavesdropper eavesdropper must make must make measurements measurements to learn about to learn about the state, but the state, but cannot do so cannot do so without without disturbance disturbance (HUP)(HUP)
Nor can the Nor can the eavesdropper eavesdropper make identical make identical copies of the copies of the state and make state and make measurements measurements on them (no-on them (no-cloning)cloning)
AttemptingAttempting either strategy either strategy will lead to will lead to errors in the errors in the detected signaldetected signal
More quantum featuresMore quantum features
SuperpositionSuperposition A quantum system can be A quantum system can be
in many states at the same in many states at the same timetime
...1
321
N
InterferenceInterference
……more powerful computersmore powerful computers
OI
A computer A computer takes some takes some input state to input state to an output statean output state
A A QuantumQuantum computer takes computer takes a a superpositionsuperposition of all possible of all possible inputs state to inputs state to a superposition a superposition of all possible of all possible output statesoutput states
Measurement Measurement results are results are random, except random, except that that interference interference (+clever (+clever algorithms) can algorithms) can reduce wrong reduce wrong answersanswers
ψ
Feynman Deutsch
EntanglementEntanglement
Separable states (not entangled)Separable states (not entangled)
2112
2121121100
2
1
1100 “Bell state”
An entangled stateAn entangled state
Foundation for most quantum information Foundation for most quantum information protocolsprotocols
Optical photons as qubitsOptical photons as qubits
|H> |V>
+|R>|D>
=i
PolarizationPolarization
Time-binTime-bin
t tt1 t2
Spatial modesSpatial modes
Freq. encodingFreq. encoding
Optical photons as qubitsOptical photons as qubits
The Good The Bad The Ugly
Single-qubit Single-qubit operationsoperations
Low Low decoherencedecoherence
High speedHigh speed
Perfect carriers Perfect carriers of quantum of quantum informationinformation
Easy to lose a Easy to lose a photonphoton
No natural No natural interactions/weak interactions/weak nonlinearities nonlinearities means 2-qubit means 2-qubit operations are operations are hardhard
Linear optics Linear optics proposals for proposals for scalable scalable quantum quantum computing are computing are extremely extremely complicated complicated
(~50-1000s of (~50-1000s of ancillas/elementancillas/elements per CNOT)s per CNOT)
Entangled Photon SourceEntangled Photon Source
“blue” photon two “red” photons
(2)
Phase matching:Phase matching:pump = s + i
kpump = ks + ki
Parametric Down-conversionParametric Down-conversion
Type-II Down-conversionType-II Down-conversion
Entangled Pair
21212
1HVVH
Correlated V-Photon
H-Photon
Confused
Recent source Recent source advancementsadvancements
High-power UV laser diodes (cheap, easy to use -> UG lab!)
Efficient single-mode coupling (long-distance, low divergence, free-space)
4-, 5-, and 6-photon entanglement Controllable entanglement – fundamental tests
and quantum computing
State of the artState of the artSource Brightness
Atomic Cascade
Downconversion
0.1
1
10
100
1000
104
105
106
107
1970
1975
1980
1985
1990
1995
2000
2005
2010
Ent
angl
ed P
air
Det
ectio
n R
ate
(Hz)
Year
0
2
4
6
8
10
1970
1975
1980
1985
1990
1995
2000
2005
2010
Num
ber
of
photo
ns
Year
Number of photons entangled
Entanglingmeasurements
Long-distance Long-distance Entanglement distributionEntanglement distribution
Quantum sourceQuantum source
Not Pictured here:FS1&2: Michael TarabaFS2: Bibiane Blauensteiner, Alessandro Fedrizzi, Christian Kurtsiefer, Tobias Schmitt-Manderbach, Henning Weier, Harald Weinfurter
Zeilinger Group
Distributing EntanglementDistributing Entanglement
Photons are the ideal carriers
Practical quantum communication needs shared entanglement over long distances
Challenges: High efficiency (no cloning) and high background rejection (single photons)
Entanglement takes to the Entanglement takes to the airair
500m
150m
Donau (Danube)
Quantum correlationsQuantum correlations
A “Bell experiment”A “Bell experiment”
Local properties (ex. A=+1, A’=-1, B=+1, Local properties (ex. A=+1, A’=-1, B=+1, B’=+1) B’=+1) A(B+B’)+A’(B-B’) = ±2A(B+B’)+A’(B-B’) = ±2
CHSH-Bell inequality (req. 16 CHSH-Bell inequality (req. 16 measurements)measurements)
S = |<AB+AB’+A’B-A’B’>| ≤ 2S = |<AB+AB’+A’B-A’B’>| ≤ 2
QM allows S = 2√2 = 2.83QM allows S = 2√2 = 2.83
SourceSet {A, A’} Set {B, B’}
+1+1
-1 -1
Freespace 1 ResultsFreespace 1 Results
Two links 500m Two links 500m & 100m& 100m
~10 ~10 coincidences/scoincidences/s
SMF-SMF SMF-SMF couplingcoupling
Time-stable Time-stable channelchannel
Measured S = 2.4 ± 0.1 (larger than 2 Measured S = 2.4 ± 0.1 (larger than 2 indicates entanglement)indicates entanglement)
Science (2003)
Polarization correlations
The next stepThe next step
500m to 7.8km (the atmosphere 500m to 7.8km (the atmosphere straight up is 7.3km thick)straight up is 7.3km thick)
No more cableNo more cable
Light passed over a city – likely real-Light passed over a city – likely real-world scenarioworld scenario
Source telescopeSource telescope
15cm
From Source
Atmospheric fluctuationsAtmospheric fluctuations
Laser source
Receiver/Movie
Test Range
FS1
4 km
HV
-45o
To detector
45o
λ/2
50/50
PBS
PBS
Receiver module
PracticalitiesPracticalities
Absence of good single-photon sourcesAbsence of good single-photon sources
Can use quantum randomness to select state:Can use quantum randomness to select state:
Triggered single photons, reduced “empty” Triggered single photons, reduced “empty” pulses |0> and double photons |2>pulses |0> and double photons |2>
Laser frequency monitoring unnecessaryLaser frequency monitoring unnecessary
VV
-45-45
4545
HH
PBS45/-45
HWP
PBS(HV)
BSAliceAlice
BBOUV
45,4545,45
VVHH
Entanglement takes to the air – Entanglement takes to the air – again!again!
Freespace 2
7.8km
ALICE BOB7.8km
V I E N N A
Time-tagging
Free-space(Quantum Channel)
ALICE BOB
Public Internet (Classical Channel)
GPSRb-clock
GPS, Rb clock
Time-tagging
BS
HWP PBS
PBS
BS
HH
PBS
HWPsPBSPol.
Pol.
VV 135135
4545
HH
VV 135135
4545
DC A
B
Freespace 2 ResultsFreespace 2 Results
S = 2.27±0.019 > 2Quantum Correlations!
Two links 7.8 km and 10Two links 7.8 km and 10-4-4kmkm
25 ccps found over time tags/internet25 ccps found over time tags/internet
Single-mode fibre to spatial-filter coupling Single-mode fibre to spatial-filter coupling
14-14-σσ Bell violation, all 16 meas. taken simultaneously Bell violation, all 16 meas. taken simultaneously
Optics Express (2005)
Remaining challengesRemaining challenges
Longer distances, Higher bit ratesLonger distances, Higher bit rates
Active components to compensate Active components to compensate atmosphereatmosphere
Long-distance quantum interference Long-distance quantum interference (repeaters)(repeaters)
Full cryptography, different protocolsFull cryptography, different protocols
Moving targets (satellites, airplanes)Moving targets (satellites, airplanes)
IQC free-space experimentIQC free-space experiment
Gregor WeihsGregor Weihs
Raymond LaflammeRaymond Laflamme
Chris ErvenChris Erven
One-way quantum computation One-way quantum computation with a multi-photon cluster statewith a multi-photon cluster state
“1”
Photonic one-way quantum Photonic one-way quantum computationcomputation
Philip Walther (ViennaPhilip Walther (ViennaHarvard)Harvard)
Terry Rudolph (Imperial)Terry Rudolph (Imperial)
Emmanuel Schenck (ViennaEmmanuel Schenck (ViennaENS)ENS)
Vlatko Vedral (Leeds)Vlatko Vedral (Leeds)
Markus Aspelmeyer (Vienna)Markus Aspelmeyer (Vienna)
Harald Weinfurter (LMU, Munich)Harald Weinfurter (LMU, Munich)
Anton Zeilinger (Vienna)Anton Zeilinger (Vienna)
QC - Circuit vs. One-way modelQC - Circuit vs. One-way model
|0
H
X
|0
|0
|0
“1”
“1”
“0”
“1”
Initialization (all qubits |0) Algorithm (dynamics) Readout(classical bits)
Circuit Model One-way model
Raussendorff & Briegel, PRL 86, 5188 (2001)
Initialization (prepare a “cluster state”)Algorithm(single-qubit measurements)
Readout(measure final qubits)
Optics: Neilsen; Browne/Rudolph
Unitary
Physical qubit
One-way quantum One-way quantum computingcomputing
Cluster states can be represented by graphsCluster states can be represented by graphs
|+ |+
CPHASE
|+ |+
|+ |+
Entanglement “bond”
00011011
000110-11
10
Processing encoded Processing encoded informationinformation
How measurement can computeHow measurement can compute
1 2
|ψ> |+>
1 2
Form a cluster state2
Measure Qubit 1 in B(α)B(α) = {|0 + eiα|1, |0 - eiα|1}
0 1
2
If “0”, do nothingIf “1”, apply NOT (bit flip)This is an example of Feed-forward
2
Qubit 2 is HRz(α)|ψ>
|ψ> Rz(α) H
Equivalent quantum circuit
More general computationsMore general computationsN
um
ber
of
en
coded
qu
bit
s
Number of operationsReadout
Making cluster statesMaking cluster states
||ψψ> > = |HHHH>+|HHVV>|HHHH>+|HHVV> +|VVHH>-|VVVV>+|VVHH>-|VVVV>
Polarizing Beam-splitterPolarizing Beam-splitter
Quantum “parity check”Quantum “parity check”
H polarization
V polarization
The four-photon clusterThe four-photon cluster
Fidelity = 63%
Quantum state tomographyReconstructed density matrix
Clusters to circuitsClusters to circuits
Horizontal bond:
1:B()
Rz(-) H
Vertical bond:
Rz(-) H
Rz(-) H
1:B()
2:B()
Clusters to circuitsClusters to circuits
Multiple circuits Multiple circuits using a single using a single clustercluster
Different order of Different order of measurementsmeasurements
One-qubit computations
Two-qubit computations
Single & two-qubit operationSingle & two-qubit operation
Single-qubit rotations Two-qubit operations
Separable Entangled
Fid ~ 83-86% Fid = 93%Tangle = 0
Fid = 84%Tangle = 0.65
Grover’s AlgorithmGrover’s Algorithm
L.K. Grover, Phys. Rev. Lett. 79, 325-328 (1997).
Easy
Sorted database Unsorted database
Hard
Best Classical: O(N) queriesQuantum: O(√N) queries
Conclusions and Future Conclusions and Future directionsdirections
First demonstration of one-way quantum computation using cluster states
Experimental Larger cluster states = more complex circuits Feed-forward – two types – easy and hard
Theoretical Different geometries and measurements Higher dimensions
SummarySummary““Real” worldReal” world First experiments demonstrating free-space First experiments demonstrating free-space
entanglement distributionentanglement distribution
Ideal worldIdeal world First demonstration of Cluster State Quantum First demonstration of Cluster State Quantum
Computing – including the first algorithmComputing – including the first algorithm
Clusters/Grover’s AlgorithmClusters/Grover’s Algorithm
90% correct computational outputFirst algorithm in the cluster model
Grover’s algorithmGrover’s algorithm
Quantum parallelismQuantum parallelism
GA initializes the qubits to equal GA initializes the qubits to equal superposition of all possible inputssuperposition of all possible inputs
Ampl
Element
000 100 111
On a query to the black box On a query to the black box (quantum database/phonebook), the (quantum database/phonebook), the sign of the amplitude of the special sign of the amplitude of the special element is flippedelement is flipped
InterferenceInterference
““Inversion about the mean” amplifies Inversion about the mean” amplifies the correct element and reduces the the correct element and reduces the othersothers
Mean
THANK YOU!THANK YOU!
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