Is it possible to assess the correct functioning of a quantum device which eludes efficient computation of the expected results? The BosonSampling protocol is one of the best candidates to experimentally demonstrate the superior computational power of quantum mechanics, but the problem of its results certification requires the development of new methodologies, when the size of the problem becomes too large for a complete classical simulation. A recent work (Walschaers et al 2016 New J. Phys. 18 032001) has provided a significant step forward in this direction, by developing a statistical test to identify particle types in a many-body interference pattern. This tool can be applied in a general scenario to assess and investigate multi-particle coherent dynamics

Fabio Sciarrino

Marco Bentivegna

Nicolò Spagnolo

New Journal of Physics

English

Abstract
               Is it possible to assess the correct functioning of a quantum device which eludes efficient computation of the expected results? The BosonSampling protocol is one of the best candidates to experimentally demonstrate the superior computational power of quantum mechanics, but the problem of its results certification requires the development of new methodologies, when the size of the problem becomes too large for a complete classical simulation. A recent work (Walschaers et al 2016 New J. Phys. 
                  18 032001) has provided a significant step forward in this direction, by developing a statistical test to identify particle types in a many-body interference pattern. This tool can be applied in a general scenario to assess and investigate multi-particle coherent dynamics.</jats:p

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Is my boson sampler working?

BENTIVEGNA, MARCO

SPAGNOLO, NICOLO'

SCIARRINO, Fabio

Archivio della ricerca- Università di Roma La Sapienza

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This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 181.59.99.152This content was downloaded on 26/06/2016 at 12:54Please note that terms and conditions apply.Is my boson sampler working?View the table of contents for this issue, or go to the journal homepage for more2016 New J. Phys. 18 041001(http://iopscience.iop.org/1367-2630/18/4/041001)Home Search Collections Journals About Contact us My IOPscienceNew J. Phys. 18 (2016) 041001 doi:10.1088/1367-2630/18/4/041001PERSPECTIVEIs my boson sampler working?MarcoBentivegna,Nicolò Spagnolo and Fabio SciarrinoQuantum Information Lab,Dipartimento di Fisica, SapienzaUniversità di Roma, Piazzale AldoMoro 5, 00185Rome, ItalyE-mail: fabio.sciarrino@uniroma1.itKeywords:Boson sampling,many-particle interference, statistical assessment, particle statisticsAbstractIs it possible to assess the correct functioning of a quantumdevice which eludes efficient computationof the expected results? The BosonSampling protocol is one of the best candidates to experimentallydemonstrate the superior computational power of quantummechanics, but the problemof its resultscertification requires the development of newmethodologies, when the size of the problembecomestoo large for a complete classical simulation. A recent work (Walschaers et al 2016New J. Phys. 18032001) has provided a significant step forward in this direction, by developing a statistical test toidentify particle types in amany-body interference pattern. This tool can be applied in a generalscenario to assess and investigatemulti-particle coherent dynamics.The strong efforts towards development of quantum simulation and computation devices aremotivated by thewidespread expectation that they should allow superpolynomial speedup for several tasks. Themost celebratedexample is given by Shor’s algorithm [1], which allows for the factorization of numbers using polynomialquantum resources. The realization of a device able to clearly demonstrate this superior computational power is,however, stillmissing. There are twomain reasons, onemore on the practical side and the othermore on theformal one. First, the technological requirements for challenging a classical device using Shor’s algorithm arestill largely out of reach. Second, the absence of efficient classical algorithms for problems such as factorizationhas not been formally demonstrated. The aimof the BosonSampling [2] (BS)protocol is to bypass these twoobstacles. It consists in simulating the evolution of n bosons through a randomunitary transformation overmspatialmodes, and in particular to sample from the corresponding output probability distribution. Thecomputational hardness of this problem is based on thewell known complexity of calculating complexmatrices’permanents [3], which finds its foundation on solid theoretical basis. At the same time, the opportunity tochallenge a classical counterpart with few tens of photons in few hundreds of spatialmodes is not too far fromcurrent technologies. Thismotivated strong experimental efforts to start providing proof-of-principleimplementations [4–12].However, all this comes at a cost. In the spirit of giving an unambiguous proof of post-classical computation,the assumptions on the internal functioning of the quantumdevice should be as few as possible. In this sense,while certifying the results of a factoring problem is trivial, complete certification of BS is not yet completelyunderstood [13]. Clearly, a brute force approach relying on comparing themeasured distributionwith theexpected onewould depend on calculating an (exponentially) large number of permanents and on collecting an(exponentially) large data sample. Another correlated problem is given by the unavoidable sparseness of adataset sample, whichwill be always present inmedium-large scale experiments. In front of these difficulties, theuse of statistical techniques has allowed, up to now, to efficiently reject the alternative hypothesis of uniformsampling [9, 10, 14]. Validations against alternative distributions, which partiallymimic the genuine BS one, aremore difficult to perform [9, 10]. In fact, the strong difference in computational complexity between problemssuch as genuine BS and, for example, sampling with distinguishable particles, is reflected infine-graineddifferences in the resulting probability distributions, which are very difficult to spot with limited-size datasets.First results have been obtained by using statistical tests which require the calculation of a small number ofpermanents [9], or by exploiting bunching properties of indistinguishable photons [10]. The use of highly-OPEN ACCESSPUBLISHED7April 2016Original content from thisworkmay be used underthe terms of the CreativeCommonsAttribution 3.0licence.Any further distribution ofthis workmustmaintainattribution to theauthor(s) and the title ofthework, journal citationandDOI.© 2016 IOPPublishing Ltd andDeutsche PhysikalischeGesellschaftsymmetric transformations is able tomagnify the differences between different particle statistics [15–17], but atthe cost of partially detaching from the original computational problem. Furthermore, a protocol to certify statepreparation by exploiting homodyne detection has been theoretically proposed in [18].A novel approach towards the certification of boson sampling experiments has nowbeen proposed in [19].The key tool behind themethod is based on state correlation functions, which store all the statistical informationon amany-particle wavefunction. In the boson sampling case, knowledge of the complete set of correlationfunctions is not fully accessible due to the computational complexity of the problem. To overcome thislimitation,Walschaers and coworkers [19]prove that relevant key properties of themany-body state can beretrieved by accessing only low-order correlation functions.More specifically, they show thatmeasuring onlytwo-mode correlators provides sufficient information to assess the nature of the input state. Indeed, differentparticle types present quantitative differences in themoments of the two-mode correlator distributions. Given acertain unitarymatrix, analytical formulas and randommatrix theory averages can be exploited to predict thesemoments, and no complex permanent calculations have to be performed. Interestingly, thismethod combinesmathematical tools common to otherfields, such asmany-body quantum theory. The statistical approach of[19] is an efficient and reliable strategy to discriminate between different particle types, such as bosons,distinguishable particles or fermions (whose evolution does not share the same complexity of bosons since it isrelated to the calculation ofmatrix determinants). Furthermore, it can be applied to exclude the case of‘simulated bosons’ [16], a physicalmodel which allows tomimic some collective bosonic properties (such asbunching and clouding [10]) by single-photon interference and phase average. Last but no least, the authorsdiscuss the experimental requirements to perform the test. Namely, they provide an argument supporting thatthe number ofmeasurements required is polynomial in n andm. The latter issue is indeed a relevant point in anyverification protocol.The results of [19] represent thefirst efficient statistical test able to identify the nature ofmany-particle statesamong a set of different hypothesis, independently from the linear unitary evolution. This opens theway for itsexperimental verificationwith current state-of-the art photonic systems, and to the potential application of themethod to recently proposed alternative boson sampling platforms [20, 21]. The achievements ofWalschaersand coworkers can lead to new perspectives, as they could be useful in thewhole quantum simulation andquantum computation field for the certification of quantumdevices. From a fundamental point of view theproposedmethod represents a thoughtful insight onmany-body interference, andmay help in shedding light onthe very properties of the different types of particle statistics.AcknowledgmentsThisworkwas supported by theH2020-FETPROACT-2014GrantQUCHIP (QuantumSimulation on aPhotonic Chip; grant agreement no. 641039, http://www.quchip.eu), and by the ERC-StartingGrant 3D-QUEST (3D-Quantum IntegratedOptical Simulation; grant agreement no. 307783, http://www.3dquest.eu).References[1] Shor PW1997 SIAM J. Comput. 26 1484[2] Aaronson S andArkhipovA 2011Proc. 43rd Annual ACMSymposium onTheory of Computing (San Jose) (NewYork: ACM) pp 333[3] Valiant LG 1979Theoretical Comput. Sci. 8 189[4] BroomeMA, Fedrizzi A, Rahimi-Keshari S, Dove J, Aaronson S, RalphTC andWhite AG2013 Science 339 794[5] Spring J B et al 2013 Science 339 798[6] TillmannM,Dakic B,HeilmannR,Nolte S, Szameit A andWalther P 2013Nature Photon 7 540Figure 1. Statistical analysis of a Boson Sampler: the particle type is identified from the output pattern of the device.2New J. Phys. 18 (2016) 041001 MBentivegna et al[7] Crespi A,OsellameR, Ramponi R, BrodD J, Galváo E F, SpagnoloN,Vitelli C,Maiorino E,Mataloni P and Sciarrino F 2013NaturePhoton 7 545[8] SpagnoloN et al 2013Phys. Rev. Lett. 111 130503[9] SpagnoloN et al 2014Nat. Photon. 8 615[10] Carolan J et al 2014Nat. Photon. 8 621[11] BentivegnaM et al 2015 Sci. Adv. 1 e1400255[12] Carolan J et al 2015 Science 349 711[13] Gogolin C, KlieschM,Aolita L andEisert J 2015 arXiv:1306.3995[14] Aaronson S andArkhipovA 2014Quantum Info. Comput. 14 1383[15] TichyMC,TierschM,Mintert F andBuchleitner A 2012New J. Phys. 14 093015[16] TichyMC,MayerK, Buchleitner A andMólmerK 2014Phys. Rev. Lett. 113 020502[17] Crespi A,OsellameR, Ramponi R, BentivegnaM, Flamini F, SpagnoloN,ViggianielloN, Innocenti L,Mataloni P and Sciarrino F 2016Nature Commun. 7 10469[18] Aolita L, Gogolin C, KlieschMandEisert J 2015Nature Commun. 6 8498[19] WalschaersM,Kuipers J, Urbina J-U,Mayer K, TichyMC,Richter K andBuchleitner A 2016New J. Phys. 18 032001[20] ShenC, Zhang Z andDuan L-M2014Phys. Rev. Lett. 112 050504[21] Peropadre B,Guerreschi GG,Huh J andAspuru-Guzik A 2015 arXiv:1510.080643New J. Phys. 18 (2016) 041001 MBentivegna et al

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