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!