tools for quantum and reversible circuit compilation
TRANSCRIPT
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ToolsForQuantumandReversibleCircuitCompilation- MARTINROETTELER- PRESENTEDBYHARSHKHETAWAT
- 11/19/2018
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Introduction/MotivationMultistagecompilationofQAlgos:◦ High leveldescriptionofprogramàNetlistsofcircuitsà Pulsesequencesà PhysicalQuantumComputer
Key:Implementclassicalsubroutines(oracles):◦ Why?◦ Underlyingproblemoften involvesclassicaldata:◦ factoring(Shor’s),◦ HHL– forsolving linearequations,◦ quantumwalks◦ quantumsimulation, etc.
◦ Howbesttoimplementonquantumcomputer?
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ReversibleComputingHowbesttoimplementclassicalsubroutines(oracles)onaquantumcomputer
Dealswith:◦ Minimizegatecountforagivenuniversalgateset◦ Minimizeresourcessuchas:◦ Circuitdepth◦ Numberofqubits required, etc.
CompilingirreversibleprogramstoQC:◦ Hideclassicalsubroutines inlibraries– optimizedcollectionoffunctions◦ Toolstoconvertclassicalcodeà networkofToffoli gates(Quipper)
LIQU|>providesREVS– tooltoautomaticallyconvertClassicalcodeà reversiblenetworks
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IdeabehindREVSBennet’smethod(1973)◦ Reverseeachtimestep◦ Performforwardcomputationusingstep-wisereversibleprocesses
◦ Copyouttheresult◦ Undoallstepsintheforwardcomputationinreverseorder
Solvesreversibleembeddingproblem◦ Cost– largememory footprint aseachintermediateresultshastobestored
◦ Solution - Bennet’s newandimprovedmethod!!(1989)
◦ Pebblegames◦ SpacevsTimetradeoff
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Usedynamicprogrammingtodeterminebeststrategyforgivenn(steps)andS(pebbles)
Worksfor1-DchainsMorecomplexforgeneralgraphs
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REVSDeterminingbeststrategyisprogramdependentandnon-trivial
REVS:◦ Booleanfunctions synthesizedusingheuristicsandoptimizations (ESOP)◦ Circuitsmadereversibleusing:◦ Bennet’s method(s)◦ Uncompute datathatisnolongerneeded (fromdatadependencies)
Forexample– SHA256◦ Nobranching, usessimpleboolean functionssuchasXOR,ANDandbitrotations◦ However, ithasinternalstatebetweenrounds
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REVSModeledusingMutableDataDependency(MDD)graphs◦ Tracksdataflowduring classingcomputation
◦ Identifywhichpartscanbeoverwritten/uncomputed (clean-up)
Clean-uponQC≅ Garbagecollectiononclassiccomputers
OutputsToffoli network◦ Imported inLIQU|>◦ Usedaspartofquantumcommunication◦ Supports compilationfordifferent targetarchitectures/abstractQCmachinemodels
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SHA-256Idealcandidate:◦ Storesstatebetweenrounds◦ Simplebinaryfunctions
4ximprovementinnumberofqubits required
Canalsobeappliedtootherhashfunctions◦ SHA-3andMD5
REVSallowsexplorationoftrade-offspace
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UsingDirtyAncillasWhataredirtyancillas?◦ Qubits inunknown state◦ Mightbeentangled inunknownway◦ Availableasscratchspace
Howcandirtyancillas beuseful?Twoscenarioscurrentlyknown:◦ MultiplycontrolledNOToperation◦ Constantincrementer |x>à |x+c>
Increment|x>by1exampleusingunknown|g>:◦ g’is2’scomplementofg=>g’– 1=not(g)◦ g+g’=0◦ |x>|g>à |x– g>|g>à |x– g>|g’– 1>à |x– g– g’+1>|g’– 1>à |x+1>|g>
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Repeat-Until-SuccessCircuitsKeyidea:Usenon-deterministiccircuits(RUScircuits)fordecomposition(Paetznick&Svore,2014)◦ Substantialreduction inTgates◦ Shorterexpectedcircuitlengthcomparedtopurelyunitarydesign◦ Approximating todesiredprecisionℇ
Hasbeenshowntoefficientlysynthesizeany1-qubitunitary
Numberofrepetitionsareprovablyfinite
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ConclusionREVS:◦ Translateclassical,irreversibleprogramsà reversiblecircuits◦ Notrequired tothink incircuitcentricmanner◦ Capturedatadependencies/mutations usingMDDs◦ Heuristicstofindoptimalpebbling strategies
Reuseofqubits evenifstateisunknown/entangled◦ Reducecircuitsizes
Implementunitaries probabilisticallyusingprotocolssuchasRUS◦ Constantfactorimprovement incircuitsize
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DiscussionReuseofdirtyancillas onlypossibleforveryspecificsituations
RUSprotocolveryinteresting:◦ Canweimplementmulti-qubit unitaries usingRUS?
Thepaperdoesn’tdiscussheuristicsusedforfindingoptimalpebblingstrategy◦ Whatheuristicsareused?◦ Canweimproveonit?