Bound States for Magic State Distillation in Fault.pdf
上传人:sy****28 上传时间:2024-09-15 格式:PDF 页数:4 大小:2.7MB 金币:15 举报 版权申诉
预览加载中,请您耐心等待几秒...

在线预览结束,喜欢就下载吧,查找使用更方便

15 金币

下载此文档

如果您无法下载资料,请参考说明:

1、部分资料下载需要金币,请确保您的账户上有足够的金币

2、已购买过的文档,再次下载不重复扣费

3、资料包下载后请先用软件解压,在使用对应软件打开

BoundStatesforMagicStateDistillationinFault-TolerantQuantumComputationEarlT.CampbellandDanE.BrowneDepartmentofPhysicsandAstronomy,UniversityCollegeLondon,GowerStreet,London,WC1E6BT,UK.Magicstatedistillationisanimportantprimitiveinfault-tolerantquantumcomputation.Themagicstatesarepurenon-stabilizerstateswhichcanbedistilledfromcertainmixednon-stabilizerstatesviaCliffordgroupoperationsalone.BecauseoftheGottesman-Knilltheorem,mixturesofPaulieigenstatesarenotexpectedtobemagicstatedistillable,butithasbeenanopenquestionwhetherallmixedstatesoutsidethissetmaybedistilled.InthisLetterweshowthat,whenresourcesarefinitelylimited,non-distillablestatesexistoutsidethestabilizeroctahedron.Inanalogywiththeboundentangledstates,whichariseinentanglementtheory,wecallsuchstatesboundstatesformagicstatedistillation.PACSnumbers:03.67.PpThesignificantnoiseanddecoherenceinquantumsystemsnumberofiterations,willalsohavenobenefit.Hence,wemeansthatharnessingthesesystemsforcomputationaltasksexplainwhyallknownprotocolsfailtodistillsomestates.mustbeperformedfaulttolerantly[1,2].InawidevarietyThesingle-qubitstabilizerstates,forwhichtheGottesman-ofsetupsonlyalimitedsetofgates,knownastheCliffordKnilltheoremapplies,arethesixpurestabilizerstates(thegroup,areimplementedinamanifestlyfaulttolerantman-eigenstatesof±X;±Yand±Z)andanyincoherentmixturener.Examplesincludesomeanyonictopologicalquantumofthese.IntheBlochsphere,thisconvexsetwith6verticescomputers[3–5],post-selectedquantumcomputers[6,7]andformsthestabilizeroctahedronpartiallyshowninfigure1a.measurementbasedtopologicalquantumcomputers[8].ThisSingle-qubitstateshavedensitymatrices:motivatestheproblemofwhensuchdevices,withpracticallyerrorfreeCliffordgates,maybepromotedtoafullquantumρ(f;a)=(11+(2f−1)(aXX+aYY+aZZ))=2;(1)computer.ThecelebratedGottesman-KnilltheoremshowsthataCliffordcircuitactingonstabilizerstates—simultane-wherea=(aX;aY;aZ)isaunitvector,andfisthefidelityouseigenstatesofseveralPaulioperators—canbeefficientlyw.r.tthepurestate