TopologicalQuantumComputation

GeorgeToh11/6/2017

Contents

• QuantumComputing• ComparisonofQCvsTQC• TopologicalQuantumComputation• HowtoimplementTQC?• Examples,progress• Industryinvestment• Futureoutlook

TimelineofQuantumComputing

• 1980s– Benioff,Manin,FeynmanandDeutsch• 1994– Shor’sAlgorithm(factoring)• 1995– Firstquantumlogicgate(trappedions)• 1997– Kitaev describesTopologicalQC• 2001– 7bitNMRQC+Shor’sAlgo:15• 2011– D-Wave128-bitQuantumAnnealer• 2013– Evidenceofnon-Abeliananyons• 2016– Google&UCSBsimulatehydrogenmolecule• 2016– IBMQX5bitQC(online!)• 2017– IBMQX16bitQC

D-Wavesystemschip

IBM7-bitchip

QuantumComputing

• Applications• Quantumfactoring(Shor’sAlgorithm)• Efficientsearch(Grover’sAlgorithm)• Quantumsimulation• Quantumsupremacy(>56Qubits)

• Qubits• Trappedions,superconductingloops,quantumdots

PioneersinTQC

• AlexeiKitaev (Caltech)• 1997- FirstproposedTopologicalquantumcomputation• 2002- ProvedthataTQCcandoanyquantumcomputation(withFreedmanandothers)

• MichaelFreedman(UCSantaBarbara)• 2005- ProposedthataquantumHalldevicecouldrealizeatopologicalqubit• DirectorofMicrosoftStationQatUCSB

Comparison– WhyTQC?

QuantumComputing• Qubits• Quantumdecoherence(Noise)• Extremelyfragile• Needtobeshieldedfromenvironmentalperturbations

TopologicalQuantumComputing• Topologicalqubitsbasedonnon-Abeliananyons• Thesetwo-dimensionalquasiparticlesformbraidswhicharemuchmorestable

Non-Abeliananyons

FermionandBoson• Abelian• Fermi-Diracstatisticsor• Bose-Einsteinstatistics

Anyon• 2-Dimensionalquasiparticle• Non-Abelian• PossibletobesomewhereinbetweenF-DandB-Estatistics• Particleinterchange:phasechangedoesnothavetobe+1or-1

TopologicalQuantumComputation

• Non-Abeliananyons• Braid=quantumoperation• Fault-tolerant

(a)and(b)aretopologicallyidentical

https://www-01.ibm.com/events/wwe/grp/grp308.nsf/vLookupPDFs/07%20Quantum%20Computing%20cognitive%20event/$file/07%20Quantum%20Computing%20cognitive%20event.pdf

Candidatesfornon-Abeliananyons

• Nanowireonsuperconductor• Majorana zeromodes

• FractionalQuantumHallStateat(fillingfactor)ν =5/2

HybridSuperconductor-SemiconductorNanowireDevices

• SemiconductorInSb nanowireincontactwithanordinarysuperconductorNb

• Zeroenergypeaksshowuponlywhenafiniteexternalmagneticfieldisappliedtothewire

2012,Science,TUDelft,Majorana Fermions

2012,NaturePhysics,WeizmannInst(Israel)

HybridSuperconductor-SemiconductorNanowireDevices

• SimilarexperimenttoDelft,publishedafewmonthslaterin2012

• InAs nanowireonAlsuperconductor

Experimentalevidenceofnon-Abeliananyons• Fabry-PerotInterferometermadeofGaAs/AlGaAsquantumwellwithaSiN layer

• PeriodofA-Boscillationindicativeofnon-Abeliannatureofν=5/2state

2013,PRL,Aharonov-Bohmoscillations

Experimentalevidenceofnon-Abeliananyons• Nextstepistoimplementandtestatwointerferometersetup

201,Quantamagazine

InvestmentsinTQC

• Microsoft:StationQ• UCSB,ProfMichaelFreedman,Theory• TUDelftandUniversityofSydney,Experimental• Purdue,ProfManfra,Experimental

• IntelandQuTech• DelftUniversity• US$50million

• BellLabs• RobertWillett

Purdue– MicrosoftStationQ

• PurdueUniversityandMicrosoftCorp.havesignedamulti-yearagreementtodevelopauseablequantumcomputer(May2017)• Growandstudyultra-puresemiconductorsandhybridsystemsofsemiconductorsandsuperconductors• Manfra’s grouphasexpertiseinatechniquecalledmolecularbeamepitaxy,usedtobuildlow-dimensionalelectronsystemsthatformthebasisforquantumbits,orqubits.

https://www.purdue.edu/newsroom/releases/2017/Q2/microsoft,-purdue-collaborate-to-advance-quantum-computing-.html

Conclusion

• Quantumcomputersarehotduetothepotentialapplications• TQCofferawaytosolvethedecoherence/noiseproblem• MicrosoftisbettingbigonTQC• TQCnotyetexperimentallydemonstrated

http://www.sciencemag.org/news/2016/12/scientists-are-close-building-quantum-computer-can-beat-conventional-one

Diracnotation

Bosons:

Fermions:

Anyons:

WhatisTopology?

• 2016NobelPrizeinPhysics• Toplogy:Inmath,describesapropertythatremainsunchangedundersmoothcontinuousdeformation

Topologicalinvariance:Tochangethetopologicalstate,alargeperturbationmakinganotherholeisrequired