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Quantum Science and Technology

Visual assessment of multi-photon interference

Fulvio Flamini, Nicolò Spagnolo, Fabio Sciarrino

Published Feb 7, 2019• 20 citations
Publisher

Abstract

Classical machine learning algorithms can provide insights on high-dimensional processes that are hardly accessible with conventional approaches. As a notable example, t -distributed Stochastic Neighbor Embedding ( t -SNE) represents the state of the art for visualization of data sets of large dimensionality. An interesting question is then if this algorithm can provide useful information also in quantum experiments with very large Hilbert spaces. Leveraging these considerations, in this work we apply t -SNE to probe the spatial distribution of n -photon events in m -dimensional Hilbert spaces, showing that its findings can be beneficial for validating genuine quantum interference in boson sampling experiments. In particular, we find that nonlinear dimensionality reduction is capable to capture distinctive features in the spatial distribution of data related to multi-photon states with different evolutions. We envisage that this approach will inspire further theoretical investigations, for instance for a reliable assessment of quantum computational advantage.

DOI
10.1088/2058-9565/ab04fc

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Classical machine learning algorithms can provide insights on high-dimensional processes that are hardly accessible with conventional approaches. As a notable example, t -distributed Stochastic Neighbor Embedding ( t -SNE) represents the state of the art for visualization of data sets of large dimensionality. An interesting question is then if this algorithm can provide useful information also in quantum experiments with very large Hilbert spaces. Leveraging these considerations, in this work we apply t -SNE to probe the spatial distribution of n -photon events in m -dimensional Hilbert spaces, showing that its findings can be beneficial for validating genuine quantum interference in boson sampling experiments. In particular, we find that nonlinear dimensionality reduction is capable to capture distinctive features in the spatial distribution of data related to multi-photon states with different evolutions. We envisage that this approach will inspire further theoretical investigations, for instance for a reliable assessment of quantum computational advantage.
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.
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.
Abstract 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.
Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.
The Boson sampling problem consists in sampling from the output probability distribution of a bosonic Fock state, after it evolves through a linear interferometer. There is strong evidence that Boson sampling is computationally hard for classical computers, while it can be solved naturally by bosons. This has led it to draw increasing attention as a possible way to provide experimental evidence for the quantum computational supremacy. Nevertheless, the very complexity of the problem makes it hard to exclude the hypothesis that the experimental data are sampled from a different probability distribution. By exploiting integrated quantum photonics, we have carried out a set of three-photon Boson sampling experiments and analyzed the results using a Bayesian approach, showing that it represents a valid alternative to currently used methods. We adopt this approach to provide evidence that the experimental data correspond to genuine three-photon interference, validating the results against fully and partially-distinguishable photon hypotheses.