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1、ATheoryofPhysicalQuantumComputation:TheQuantumComputerConditionGeraldGilbert,MichaelHamrickandF.JavierThayer∗†QuantumInformationScienceGroupMitre260IndustrialWayWest,Eatontown,NJ07724USAAbstract.Inthispaperwepresentanewunifiedtheoreticalframeworkthatdescribesthefulldynamicsofquantumcompu
2、tation.Ourformulationallowsanyquestionspertainingtothephysicalbehaviorofaquantumcomputertobeframed,andinprinciple,answered.Werefertothecentralorganizingprin-cipledevelopedinthispaper,onwhichourtheoreticalstructureisbased,astheQuantumComputerCondition(QCC),arigorousmathematicalstatementt
3、hatconnectstheirreversibledynamicsofthequantumcomputingmachine,withthereversibleoperationsthatcomprisethequantumcomputationin-tendedtobecarriedoutbythequantumcomputingmachine.ArmedwiththeQCC,wederiveapowerfulresultthatwecalltheEncodingNo-GoTheorem.Thistheoremgivesaprecisemathematicalsta
4、tementoftheconditionsunderwhichfault-tolerantquantumcomputationbecomesimpossibleinthepres-enceofdissipationand/ordecoherence.Inconnectionwiththistheorem,weexplicitlycalculateauniversalcriticaldampingvalueforfault-tolerantquan-tumcomputation.Inadditionweshowthattherecently-discoveredappr
5、oachtoquantumerrorcorrectionknownas“operatorquantumerror-correction”isaspecialcaseofourmoregeneralformulation.Ourapproachfurnisheswhatwewillrefertoas“operatorquantumfault-tolerance.”Inparticular,weshowhowtheQCCallowsonetoderiveerrorthresholdsforfaulttoleranceinacompletelygeneralcontext.
6、Weprovetheexistenceofsolutionstoaclassoftime-dependentgeneralizationsoftheLindbladequation.UsingtheQCC,wearXiv:quant-ph/0507141v220Jul2005alsoshowthattheseeminglydifferentcircuit,graph-(includingcluster-)state,andadiabaticparadigmsforquantumcomputingareinfactallmanifestationsofasingle,un
7、iversalparadigmforallphysicalquantumcomputation.∗ResearchsupportedunderMITRETechnologyProgramGrant51MSR211.†E-mailaddress:{ggilbert,mhamrick,jt}@mitre.org12GERALDGILBERT,MICHAELHAMRICKANDF.JAVIERTHAYERContents1.Introduction22.TheQuantumComputerCondition33.TheEncodingNo-GoTheore
