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arXiv:1809.01953

Classical simulability of noisy boson sampling

Jelmer J. Renema, V. S. Shchesnovich, Raúl García−Patrón

Published Sep 6, 2018• 29 citations
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Abstract

Quantum mechanics promises computational powers beyond the reach of classical computers. Current technology is on the brink of an experimental demonstration of the superior power of quantum computation compared to classical devices. For such a demonstration to be meaningful, experimental noise must not affect the computational power of the device; this occurs when a classical algorithm can use the noise to simulate the quantum system. In this work, we demonstrate an algorithm which simulates boson sampling, a quantum advantage demonstration based on many-body quantum interference of indistinguishable bosons, in the presence of optical loss. Finding the level of noise where this approximation becomes efficient lets us map out the maximum level of imperfections at which it is still possible to demonstrate a quantum advantage. We show that current photonic technology falls short of this benchmark. These results call into question the suitability of boson sampling as a quantum advantage demonstration.

DOI
10.48550/arxiv.1809.01953

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Quantum mechanics promises computational powers beyond the reach of classical computers. Current technology is on the brink of an experimental demonstration of the superior power of quantum computation compared to classical devices. For such a demonstration to be meaningful, experimental noise must not affect the computational power of the device; this occurs when a classical algorithm can use the noise to simulate the quantum system. In this work, we demonstrate an algorithm which simulates boson sampling, a quantum advantage demonstration based on many-body quantum interference of indistinguishable bosons, in the presence of optical loss. Finding the level of noise where this approximation becomes efficient lets us map out the maximum level of imperfections at which it is still possible to demonstrate a quantum advantage. We show that current photonic technology falls short of this benchmark. These results call into question the suitability of boson sampling as a quantum advantage demonstration.
Bosonic many-body systems are prominent candidates for a quantum advantage demonstration, with the most popular approaches being either a quantum simulation beyond the reach of current classical computers, or a demonstration of boson sampling. It is a crucial open problem to understand how resilient such quantum advantage demonstrations are to imperfections such as boson loss and particle distinguishability. We partially solve this problem by showing that imperfect multi-boson interference can be efficiently approximated as ideal interference of groups of smaller number of bosons, where the other particles interfere classically. Crucially, the number of bosons undergoing interference in our approxmation only depends on the level of imperfections, but is independent of the actual number of particles. This allows us to construct a simple but stringent benchmark for comparing many-body bosonic technological platforms.
As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS-in the form of an inequality between the input squeezing parameter, the overall transmission rate, and the quality of photon detectors. Our result serves as a nonclassicality test that must be passed by any quantum computational supremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.
Boson sampling stands out as a promising approach toward experimental demonstration of quantum computational advantage. However, the presence of physical noise in near-term experiments hinders the realization of quantum computational advantage with boson sampling. Since physical noise in near-term boson-sampling devices is inevitable, precise characterization of the boundary of noise rates where the classical intractability of boson sampling is maintained is crucial for quantum computational advantage using near-term devices. In this work, we identify the level of partial-distinguishability noise that upholds the classical intractability of boson sampling. We find that boson sampling with on average O ( log  N ) distinguishable photons out of N input photons maintains the equivalent complexity to the ideal boson-sampling case. By providing strong complexity-theoretical evidence for the classical intractability of noisy boson sampling, we expect that our findings will ultimately facilitate the demonstration of quantum computational advantage with noisy boson-sampling experiments in the near future.
Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and imperfections, such as loss in the interferometer and random counts at the detectors, could challenge the sampling task from entering the regime where quantum advantage is achievable. In this work we introduce higher-order nonlinearities as a means to enhance the computational complexity of the problem and the protocol's robustness against noise, i.e., to increase the noise threshold that allows us to perform an efficient classical simulation of the problem. Using a phase-space method based on the negativity volume of the relevant quasiprobability distributions, we establish a necessary nonclassicality condition that any experimental proof of quantum advantage must satisfy. Our results indicate that the addition of single-mode Kerr nonlinearity at the input-state preparation level, while retaining a linear-optical evolution, makes the boson-sampling protocol more robust against noise and consequently relaxes the constraints on the noise parameters required to show quantum advantage.
Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.
Experimental demonstration of the quantum advantage over classical simulations with Boson Sampling is currently under intensive investigation. There seems to be a scalability issue to the necessary number of bosons on the linear optical platforms and the experiments, such as the recent Boson Sampling with 20 photons on 60-port interferometer by H. Wang et al., Phys. Rev. Lett.123 (2019) 250503, are usually carried out on a small interferometer, much smaller than the size necessary for the no-collision regime. Before demonstration of quantum advantage, it is urgent to estimate exactly how the classical computations necessary for sampling from the output distribution of Boson Sampling are reduced when a smaller-size interferometer is used. This work supplies such a result, valid with arbitrarily close to 1 probability, which reduces in the no-collision regime to the previous estimate by Clifford and Clifford. One of the results with immediate application to current experiments with Boson Sampling is that classically sampling from the interference of [Formula: see text] single bosons on an [Formula: see text]-port interferometer is at least as hard as that with [Formula: see text] single bosons in the no-collision regime, i.e. on a much larger interferometer with at least [Formula: see text] ports.