5AchievementsThelanguageQuipperhasbeendesignedinthecontextoftheIARPAfundedQCSprogram8SevenalgorithmswereusedasbenchmarksThesealgorithmswerechosenbyIARPAtoprovideareasonablyrepresentativecrosssec ID: 408518
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N.J.Ross,P.Selinger,J.M.SmithandB.Valiron3Tworun-times.AQuipperprogramdescribesafamilyofcircuits,whichmaydependonsomeclassicalparameters.Aftercompilation,aprogramisrstexecutedtogenerateacircuit(circuitgenerationtime),andthenthecircuitisexecuted(circuitexecutiontime).Parameter/inputdistinction.Quipperhastwonotionsofclassicaldata:parameters,whichareknownatcircuitgenerationtime,andinputs,whichareknownatcircuitexecutiontime.Forexample,thetypeBoolstandsforparametersandthetypeBitforinputs.Extensibledatatypes.QuipperoffersanabstractviewofthenotionofquantumdatausingthepowerfultypeclassmechanismofHaskell'stypesystem.Automaticgenerationofquantumoracles.Concretequantumalgorithmscomewithnon-trivialclassicaloperationsthathavetobeliftedtoquantumoperations.QuippercomeswithafacilitytoturnordinaryHaskellprogramsintoreversiblecircuits,usingTemplateHaskell.SimilarlytowhatisdoneinLava[3],thesemanticsofcircuitgenerationiscapturedinamonad.Thispermitsbothimperative-styleprogramming,whereacircuitisdescribedgatebygate,anddeclarative-style,wherecircuitsaremanipulatedasrst-classobjects,andtransformedwithcombinators.Anexampleofcodewiththecorrespondingcircuitisshownbelow.circ::Qubit�-CircQubitcircx=dohadamard_atxwith_ancilla$\y�-doqnot_atyqnotx`controlled`yqnot_atyhadamard_atxreturnx 5AchievementsThelanguageQuipperhasbeendesignedinthecontextoftheIARPA-fundedQCSprogram[8].Sevenalgorithmswereusedasbenchmarks.ThesealgorithmswerechosenbyIARPAtoprovideareasonablyrepresentativecross-sectionofcurrentalgorithms.BinaryWeldedTree(BWT).Tondalabelednodeinagraph[2].BooleanFormula(BF).ToevaluateaNANDformula[1].Theversionofthisalgorithmimple-mentedinQuippercomputesawinningstrategyforthegameofHex.ClassNumber(CL).Toapproximatetheclassgroupofarealquadraticnumbereld[6].GroundStateEstimation(GSE).Tocomputethegroundstateenergylevelofaparticularmolecule[14].QuantumLinearSystems(QLS).Tosolvealinearsystemofequations[7].UniqueShortestVector(USV).Tochoosetheshortestvectoramongagivenset[13].TriangleFinding(TF).Toexhibitatriangleinsideadensegraph[11].Thesealgorithmsuseofawidevarietyofquantumprimitives,suchasamplitudeamplication,quantumwalks,thequantumFouriertransform,andquantumsimulation.Severalofthemalsorequiretheimple-mentationofcomplexclassicaloracles.ThestartingpointforeachofouralgorithmimplementationswasadetaileddescriptionofthealgorithmprovidedbyIARPA.TheywereallcodedinQuipperandarerunning,inthesensethatonecangeneratethecircuit(andportionthereof).UsingQuipper,wewereabletoperformsemi-orcompletelyautomatedlogicalgatecountestima-tionsforeachofthealgorithms.Forexample,inthecaseofthetrianglendingalgorithm,./tf-fgatecount-oorthodox-l31-n15-r6producesthegatecountforthecompletealgorithm.Thisrunstocompletioninundertwominutesonalaptopcomputer,andproducesacountof30,189,977,982,990(over30trillion)totalgatesand4676qubits.