Sombrero Adiabatic Quantum Computation: a heuristic - PDF document

Sombrero Adiabatic Quantum Computation: a heuristic strateg for quantum adiabatic evolution Workshop on Complexity Resources in Physical Computation Oxford University Computing Laboratory Salvador Elías Venegas Andraca Agenda Agenda 1 Contribution 1 . 2.Motivations.3.NP-com p p p 4.Basicsofquantumadiabaticalgorithms.5.Results. Motivation(Perdomo,VenegasAndraca Computersplayakeyroleinmodernsocietyforitspotential science science Iiil dii lih i t i a l i onsp y acentra i h development/execution.Whetherwechooserandominitialconditionsornotdependsonourexpertiseontheparticular applicationfield. asmuchknowled einadvanceas ossiblecouldbe crucialinalgorithmexecutiontime. Motivation(mygroup) MyresearchgroupinMexicoisfocusingonquantumalgorithmssimulationondesktopanddistributedcomputerplatforms.The algorithms algorithms contributiontomygroup’sexpertise. simulatequantumalgorithmsintheircomputercloud. Examples of the importance of initial conditions in applied computer ProteinFoldingProblem:Nature’slectureOptimizationmethods Given the amino acid sequence of a protein, predict its compact three-dimensional native state Shti di f lbl ti S c h ti agramo f b u l arpro i IntroductiontoProteinStructure.C.BrandenandJ.Tooze.TaylorandFrancis(1999). The Protein Folding problem is a key challenge in modern science for both its intrinsic importance in the foundations of biological i d it liti i dii ilt d sc d it ons me c i ne, agr i other areas. completeproblems TwoequivalentwaystodefineanNP-completeproblem: problem problem nondeterministicTuringmachine. A for polynomialtimebyaTuringmachine. SolvingNP-completeproblemsiscrucialforboththeoretical andapplicationpurposes. Quantumadiabaticalgorithms ThequantumadiabaticmodelofcomputationwasoriginallyproposedbyE.Farhi,J.Goldstone,S.GutmannandM.Sipser, and has : and has : Quantumadiabaticalgorithms )()|()(|^ttHdttdi H t H t H ^^^ 1 ) ( where pb H T H T t H 1 ) ( T T ttl Hamiltonian Hamiltonian,encodes ground T i s e t o t a l ng quantumalgorithm Hamiltonian a easy prepare groundstate.problemstudy. Quantumadiabaticalgorithms 3.IfweletthesystemrunforsufficientlylongtimeT,thequantum dibti lith t dit tht h i a a b a owsus opre t a t enmeasur t ofthesystemdescribedby ) ( ^ t H WeshallbeveryclosetothegroundstateoftheHamiltonian ) ( t pH^ which,bydefinition,hasthesolutiontotheproblemencodedinitsgroundstate! SombreroAdiabaticQuantumComputation Perdomo,VenegasAndraca Wedivergefromtheconventionalideaofstartingquantumadiabatic orithmswithauniformsu p er p ositionstate. g Instead,ourproposedalgorithm,namedSombreroAdiabaticQuantum utation startswithaninitial g uessthatcanbe chosenatwillorfollowingintuitionabouttheproblem Weprovideaproo f conceptforsombrero-AQCandthepotentialusefulnessofstartingwithaguessstatefortheadiabaticevolutionbyperforminganexhaustivenumericalstudyonhard-to-satisfysixand ibl v e i nstanceso h e3-SA em,an ngourresu withtheconventionalAQCapproach. SombreroAdiabaticQuantumComputation Fortheadiabaticevolutioninaconventional-AQCalgorithm,oneconnectsthroughalinearrampaninitialHamiltonianwiththefinal Hamiltonian Hamiltonian ForsombreroAQC,thetime-dependentHamiltoniancanbewrittenas fisombreroHT t onperturbatiHT t hatHT t tH^^^^)(1)( Wherethehatfunctionmayhavetheform: Thehatfunctionmustturnoffthe Hamiltonianatt=0andt=T. t/T(1-t/T) SombreroAdiabaticQuantumComputation 6binaryvariables binary variables 000000...USA instances 111111 111111...All g uesses instances 000000 111111... 10.0... g Values of 0.5 10.0... 0.5 10.0... 0.5 10.0... for six binar y variables Wegenerated23-SATuniquesatisfyingassignmentinstances,eachhavingasitsonlysolutiononeofthe2possibleassignments.All2instanceshaveadifferentstateas SAT 2 7 3 - SAT unique SombreroAdiabaticQuantumComputation Mindthegap! Summaryofthe327,680calculationsfor7variable3SATinstancesofminimum-gap medianvaluesasfunctionofthetransversefieldintensitywithingroupssortedbynumberofbitips(BF)[(a)]andnumberofunsatisedclauses(UC)[(b)].Plotsincludethe128calculationsusingconventional-AQC(Eq.2). Focuson:-Bette valuesthanConventionalQAC. -Randominitialconditions.-Roleoftransversefieldintensity. futureresearchdirections 1.3-SATisnotthebestchoiceforastudyoninitialconditions.We most most completeproblems.FarhietalandVanDametalhavestudieditunderthelightofquantumadiabaticalgorithms. Thus,nextstepsincluderesearchonTSPandproteinFolding. Sffii dii fll dibii S u c i entcon i a a b i t y arest erstu Weonlyfocusedonminimumgap. 3.Infutureresearchefforts,weshallstudyotheradiabaticityconditions(forexample,whetherepsilontrulyscales rtin utsize p )