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arXiv:1312.3080 · Physical Review Letters

Stringent and Efficient Assessment of Boson-Sampling Devices

Malte C. Tichy, Klaus Mayer, Andreas Buchleitner, Klaus Mølmer

Published Jul 9, 2014• 127 citations
arXivHTMLPDF

Abstract

Boson sampling holds the potential to experimentally falsify the extended Church-Turing thesis. The computational hardness of boson sampling, however, complicates the certification that an experimental device yields correct results in the regime in which it outmatches classical computers. To certify a boson sampler, one needs to verify quantum predictions and rule out models that yield these predictions without true many-boson interference. We show that a semiclassical model for many-boson propagation reproduces coarse-grained observables that are proposed as witnesses of boson sampling. A test based on Fourier matrices is demonstrated to falsify physically plausible alternatives to coherent many-boson propagation.

DOI
10.1103/physrevlett.113.020502

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Boson sampling holds the potential to experimentally falsify the extended Church-Turing thesis. The computational hardness of boson sampling, however, complicates the certification that an experimental device yields correct results in the regime in which it outmatches classical computers. To certify a boson sampler, one needs to verify quantum predictions and rule out models that yield these predictions without true many-boson interference. We show that a semiclassical model for many-boson propagation reproduces coarse-grained observables that are proposed as witnesses of boson sampling. A test based on Fourier matrices is demonstrated to falsify physically plausible alternatives to coherent many-boson propagation.
A boson sampling device could efficiently sample from the output probability distribution of noninteracting bosons undergoing many-body interference. This problem is not only classically intractable, but its solution is also believed to be classically unverifiable. Hence, a major difficulty in experiment is to ensure a boson sampling device performs correctly. We present an experimental friendly scheme to extract useful and robust information from the quantum boson samplers based on coarse-grained measurements. The procedure can be applied to certify the equivalence of boson sampling devices while ruling out alternative fraudulent devices. We perform numerical simulations to demonstrate the feasibility of the method and consider the effects of realistic noise. Our approach is expected to be generally applicable to other many-body certification tasks beyond the boson sampling problem.
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Boson samplers-set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modespromise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science.However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles?Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device.We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns.The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.
Boson samplers-set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modes-promise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles? Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device. We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns. The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.
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.
Boson sampling can provide strong evidence that the computational power of a quantum computer outperforms a classical one via currently feasible linear optics experiments. However, how to identify an actual boson sampling device against any classical computing imposters is an ambiguous problem due to the computational complexity class in which boson sampling lies. The certification protocol based on bosonic bunching fails to rule out the so-called mean-field sampling. We propose a certification scheme to distinguish the boson sampling from the mean-field sampling for any random scattering matrices chosen via the Harr-measure. We numerically analyze our scheme and the influence of imperfect input states caused by non-simultaneous arrival photons.