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Quantum Information and Measurement (QIM)

Validation of multi-photon interference in photonic boson sampling

Taira Giordani, Fulvio Flamini, Matteo Pompili, Niko Viggianiello, Nicolò Spagnolo, Fabio Sciarrino, Andrea Crespi, Roberto Osellame, Nathan Wiebe, Mattia Walschaers, Andreas Buchleitner

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Multi-photon interference is believed to have a fundamental role for obtaining a quantum advantage. In this work we discuss a reliable and efficient technique to find a signature of its presence in boson sampling experiments.
DOI
10.1364/qim.2019.s2c.6

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The progressive development of quantum technologies in many areas, ranging from investigation on foundamentals of quantum of mechanics to quantum information and computation, has increased the interest on those problems that can exhibit a quantum advantage. The Boson Sampling problem is a clear example where traditional computers fail in the task of sampling from the distribution of n indistinguishable photons after a propagation in a m-mode optical interferometer. In this context, in the absence of classical algorithms able to simulate efficiently multi-photon interference, the validation of Boson Sampling is still an open problem. Here we investigate a novel approach to Boson Sampling validation based on statistical properties of correlation functions. In particular we discuss its feasibility in actual proof-of-principle experiments. Furthermore we provide an extensive study of the physical resources required to validate experiments, investigating also the role of bosonic bunching in high-dimensional applications. Our investigation confirms the goodness of the validation protocol, paving the way to use this toolbox for the validation of Boson Sampling devices.
It is strongly believed that the evolution of bosons undergoing arbitrary linear unitary transformations quickly becomes hard to predict using classical computers as we increase the number of particles and modes. Photons propagating in a multiport interferometer naturally solve this so-called boson sampling problem: sample the outputs of a multi-photon experiment in a linear-optical interferometer. This motivates the development of technologies that enable precise control of multiphoton interference in large interferometers.
Multi-particle interference is a key resource for quantum information processing, as exemplified by Boson Sampling. Hence, given its fragile nature, an essential desideratum is a solid and reliable framework for its validation. However, while several protocols have been introduced to this end, the approach is still fragmented and fails to build a big picture for future developments. In this work, we propose an operational approach to validation that encompasses and strengthens the state of the art for these protocols. To this end, we consider the Bayesian hypothesis testing and the statistical benchmark as most favorable protocols for small- and large-scale applications, respectively. We numerically investigate their operation with finite sample size, extending previous tests to larger dimensions, and against two adversarial algorithms for classical simulation: the mean-field sampler and the metropolized independent sampler. To evidence the actual need for refined validation techniques, we show how the assessment of numerically simulated data depends on the available sample size, as well as on the internal hyper-parameters and other practically relevant constraints. Our analyses provide general insights into the challenge of validation, and can inspire the design of algorithms with a measurable quantum advantage.