ToolsForQuantumandReversibleCircuitCompilation- MARTINROETTELER- PRESENTEDBYHARSHKHETAWAT

- 11/19/2018

Introduction/MotivationMultistagecompilationofQAlgos:◦ High leveldescriptionofprogramàNetlistsofcircuitsà Pulsesequencesà PhysicalQuantumComputer

Key:Implementclassicalsubroutines(oracles):◦ Why?◦ Underlyingproblemoften involvesclassicaldata:◦ factoring(Shor’s),◦ HHL– forsolving linearequations,◦ quantumwalks◦ quantumsimulation, etc.

◦ Howbesttoimplementonquantumcomputer?

ReversibleComputingHowbesttoimplementclassicalsubroutines(oracles)onaquantumcomputer

Dealswith:◦ Minimizegatecountforagivenuniversalgateset◦ Minimizeresourcessuchas:◦ Circuitdepth◦ Numberofqubits required, etc.

CompilingirreversibleprogramstoQC:◦ Hideclassicalsubroutines inlibraries– optimizedcollectionoffunctions◦ Toolstoconvertclassicalcodeà networkofToffoli gates(Quipper)

LIQU|>providesREVS– tooltoautomaticallyconvertClassicalcodeà reversiblenetworks

IdeabehindREVSBennet’smethod(1973)◦ Reverseeachtimestep◦ Performforwardcomputationusingstep-wisereversibleprocesses

◦ Copyouttheresult◦ Undoallstepsintheforwardcomputationinreverseorder

Solvesreversibleembeddingproblem◦ Cost– largememory footprint aseachintermediateresultshastobestored

◦ Solution - Bennet’s newandimprovedmethod!!(1989)

◦ Pebblegames◦ SpacevsTimetradeoff

Usedynamicprogrammingtodeterminebeststrategyforgivenn(steps)andS(pebbles)

Worksfor1-DchainsMorecomplexforgeneralgraphs

REVSDeterminingbeststrategyisprogramdependentandnon-trivial

REVS:◦ Booleanfunctions synthesizedusingheuristicsandoptimizations (ESOP)◦ Circuitsmadereversibleusing:◦ Bennet’s method(s)◦ Uncompute datathatisnolongerneeded (fromdatadependencies)

Forexample– SHA256◦ Nobranching, usessimpleboolean functionssuchasXOR,ANDandbitrotations◦ However, ithasinternalstatebetweenrounds

REVSModeledusingMutableDataDependency(MDD)graphs◦ Tracksdataflowduring classingcomputation

◦ Identifywhichpartscanbeoverwritten/uncomputed (clean-up)

Clean-uponQC≅ Garbagecollectiononclassiccomputers

OutputsToffoli network◦ Imported inLIQU|>◦ Usedaspartofquantumcommunication◦ Supports compilationfordifferent targetarchitectures/abstractQCmachinemodels

SHA-256Idealcandidate:◦ Storesstatebetweenrounds◦ Simplebinaryfunctions

4ximprovementinnumberofqubits required

Canalsobeappliedtootherhashfunctions◦ SHA-3andMD5

REVSallowsexplorationoftrade-offspace

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>

Repeat-Until-SuccessCircuitsKeyidea:Usenon-deterministiccircuits(RUScircuits)fordecomposition(Paetznick&Svore,2014)◦ Substantialreduction inTgates◦ Shorterexpectedcircuitlengthcomparedtopurelyunitarydesign◦ Approximating todesiredprecisionℇ

Hasbeenshowntoefficientlysynthesizeany1-qubitunitary

Numberofrepetitionsareprovablyfinite

ConclusionREVS:◦ Translateclassical,irreversibleprogramsà reversiblecircuits◦ Notrequired tothink incircuitcentricmanner◦ Capturedatadependencies/mutations usingMDDs◦ Heuristicstofindoptimalpebbling strategies

Reuseofqubits evenifstateisunknown/entangled◦ Reducecircuitsizes

Implementunitaries probabilisticallyusingprotocolssuchasRUS◦ Constantfactorimprovement incircuitsize

DiscussionReuseofdirtyancillas onlypossibleforveryspecificsituations

RUSprotocolveryinteresting:◦ Canweimplementmulti-qubit unitaries usingRUS?

Thepaperdoesn’tdiscussheuristicsusedforfindingoptimalpebblingstrategy◦ Whatheuristicsareused?◦ Canweimproveonit?