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arXiv:2411.14076

Sample space filling analysis for boson sampling validation

A. A. Mazanik, A. N. Rubtsov

Published Nov 21, 2024• 0 citations
arXivHTMLPDF

Abstract

Achieving a quantum computational advantage regime, and thus providing evidence against the extended Church-Turing thesis, remains one of the key challenges of modern science. Boson sampling seems to be a very promising platform in this regard, but to be confident of attaining the advantage regime, one must provide evidence of operating with a correct boson sampling distribution, rather than with a pathological classically simulatable one. This problem is often called the validation problem, and it poses a major challenge to demonstrating unambiguous quantum advantage. In this work, using the recently proposed wave function network approach, we study the sample space filling behavior with increasing the number of collected samples. We show that due to the intrinsic nature of the boson sampling wave function, its filling behavior can be computationally efficiently distinguished from classically simulated cases. Therefore, we propose a new validation protocol based on the sample space filling analysis and test it for problems of up to $20$ photons injected into a $400$-mode interferometer. Due to its simplicity and computational efficiency, it can be used among other protocols to validate future experiments to provide more convincing results.

DOI
10.48550/arxiv.2411.14076

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Achieving a quantum computational advantage regime, and thus providing evidence against the extended Church-Turing thesis, remains one of the key challenges of modern science. Boson sampling seems to be a very promising platform in this regard, but to be confident of attaining the advantage regime, one must provide evidence of operating with a correct boson sampling distribution, rather than with a pathological classically simulatable one. This problem is often called the validation problem, and it poses a major challenge to demonstrating unambiguous quantum advantage. In this work, using the recently proposed wave function network approach, we study the sample space filling behavior with increasing the number of collected samples. We show that due to the intrinsic nature of the boson sampling wave function, its filling behavior can be computationally efficiently distinguished from classically simulated cases. Therefore, we propose a new validation protocol based on the sample space filling analysis and test it for problems of up to 202020 photons injected into a 400400400-mode interferometer. Due to its simplicity and computational efficiency, it can be used among other protocols to validate future experiments to provide more convincing results.
A universal quantum computer of moderate scale is not available yet, however intermediate models of quantum computation would still permit demonstrations of a quantum computational advantage over classical computing and could challenge the Extended Church-Turing Thesis. One of these models based on single photons interacting via linear optics is called Boson Sampling. Proof-of-principle Boson Sampling has been demonstrated, but the number of photons used for these demonstrations is below the level required to claim quantum computational advantage. To make progress with this problem, here we conclude that the most practically achievable pathway to scale Boson Sampling experiments with current technologies is by combining continuous-variables quantum information and temporal encoding. We propose the use of switchable dual-homodyne and single-photon detections, the temporal loop technique and scattershot based Boson Sampling. This proposal gives details as to what the required assumptions are and a pathway for a quantum optical demonstration of quantum computational advantage. Furthermore, this particular combination of techniques permits a single efficient implementation of Boson Sampling and efficient verification in a single experimental setup.
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A universal quantum computer of moderate scale is not available yet, however intermediate models of quantum computation would still permit demonstrations of a quantum computational advantage over classical computing and could challenge the Extended Church-Turing Thesis. One of these models based on single photons interacting via linear optics is called Boson Sampling. Proof-of-principle Boson Sampling has been demonstrated, but the number of photons used for these demonstrations is below the level required to claim quantum computational advantage. To make progress with this problem, here we conclude that the most practically achievable pathway to scale Boson Sampling experiments with current technologies is by combining continuous-variables quantum information and temporal encoding. We propose the use of switchable dual-homodyne and single-photon detections, the temporal loop technique and scattershot based Boson Sampling. This proposal gives details as to what the required assumptions are and a pathway for a quantum optical demonstration of quantum computational advantage. Furthermore, this particular combination of techniques permits a single efficient implementation of Boson Sampling and efficient verification in a single experimental setup.
Boson sampling is a computational problem that has recently been proposed as a candidate to obtain an unequivocal quantum computational advantage. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. We review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. We also discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered, and advances in the development of suitable techniques for validation of boson sampling experiments. We conclude by discussing the future application of photonic boson sampling devices beyond the original theoretical scope.
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