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1、TheAdiabaticTheoreminthePresenceofNoiseMichaelJ.O’Hara∗andDianneP.O’Leary†February3,2008AbstractWeproviderigorousboundsfortheerroroftheadiabaticapproximationofquan-tummechanicsunderfoursourcesofexperimentalerror:perturbationsintheini-tialcondition,systematictime-dependentperturbationsintheHamilto
2、nian,couplingtolow-energyquantumsystems,anddecoherenttime-dependentperturbationsintheHamiltonian.Fordecoherentperturbations,wefindbothupperandlowerboundsontheevolutiontimetoguaranteetheadiabaticapproximationperformswithinapre-scribedtolerance.Ournewresultsincludeexplicitdefinitionsofconstants,andwe
3、applythemtothespin-1/2particleinarotatingmagneticfield,andtothesupercon-ductingfluxqubit.Wecomparethetheoreticalboundsonthesuperconductingfluxqubittosimulationresults.1IntroductionAdiabaticquantumcomputation[7](AQC)isamodelofquantumcomputationequivalenttothestandardmodel[1].Aphysicalsystemisslowlyev
4、olvedfromthegroundstateofasimplesystem,toonewhosegroundstateencodesthesolutiontothedifficultproblem.Byaphysicalprincipleknownastheadiabaticapproximation,iftheevolutionisdonesufficientlyslowly,andtheminimumenergygapseparatingthegroundstatefromhigherstatesissufficientlylarge,thenthefinalstateofthesystemsh
5、ouldbethestateencodingthesolutiontosomearXiv:0801.3872v1[quant-ph]25Jan2008problem.Thebiggesthurdlesfacingmanypotentialimplementationsofaquantumcomputeraretheerrorsduetointeractionofthequbitswiththeenvironment.However,theeffectsofsucherrorsaredifferentinAQCthaninstandardquantumcomputing.AQCisrobust
6、against∗GraduatestudentinAppliedMathematics,UniversityofMarylandatCollegePark(mjo-hara@gmail.com)†DepartmentofComputerScienceandInstituteforAdvancedComputerStudies,UniversityofMaryland;andNationalInstituteofStandardsandTechnology,MathematicalandComputationalSciencesDivision,Gaithersburg,Maryland.
7、Email:oleary@cs.umd.edu.ResearchsupportedinpartbyNationalScienceFoundationGrantCCF0514213.1dephasinginthegroundstate,forinstance[5],andsomehavesuggestedthatnoiseinsomeregimesmightactuallyassistadiabaticquantumcomputati
