Topological Quantum Computation George Toh 11/6/2017
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