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arXiv:2501.13433 · PRX Quantum

Quantum Computational Advantage of Noisy Boson Sampling with Partially Distinguishable Photons

Byeongseon Go, Changhun Oh, Hyunseok Jeong

Published Aug 15, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/rflv-gc66

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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.
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.
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Boson Sampling, a computational task believed to be classically hard to simulate, is expected to hold promise for demonstrating quantum computational advantage using near-term quantum devices. However, noise in experimental implementations poses a significant challenge, potentially rendering Boson Sampling classically simulable and compromising its classical intractability. Numerous studies have proposed classical algorithms that can efficiently simulate Boson Sampling under various noise models, particularly as noise rates increase with circuit depth. To address this challenge, we investigate the viability of achieving quantum computational advantage through Boson Sampling implemented with shallow-depth linear optical circuits. In particular, as the average-case hardness of estimating output probabilities of Boson Sampling is a crucial ingredient in demonstrating its classical intractability, we make progress on establishing the average-case hardness of Boson Sampling confined to logarithmic-depth regimes. We also obtain the average-case hardness for logarithmic-depth Fock-state Boson Sampling subject to lossy environments and for the logarithmic-depth Gaussian Boson Sampling. By providing complexity-theoretical backgrounds for the classical simulation hardness of logarithmic-depth Boson Sampling, we expect that our findings will mark a crucial step towards a more noise-tolerant demonstration of quantum advantage with shallow-depth Boson Sampling.
We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed with photons of partial distinguishability. We find conditions for which this algorithm is efficient, which gives a lower limit on the required indistinguishability to demonstrate a quantum advantage. Under these conditions, adding more photons only polynomially increases the computational cost to simulate a boson sampling experiment.
Abstract Boson sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of ‘quantum computational supremacy’, this motivates optimising classical simulation schemes for a realistic model of the problem, in this case boson sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of boson sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised boson sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches.
We present a classical algorithm that approximately samples from the output distribution of certain noisy Boson Sampling experiments. This algorithm is inspired by a recent result of Aharonov, Gao, Landau, Liu and Vazirani and makes use of an observation originally due to Kalai and Kindler that the output probability of Boson Sampling experiments with a Gaussian noise model can be approximated by sparse low-degree polynomials. This observation alone does not suffice for classical sampling, because its marginal probabilities might not be approximated by sparse low-degree polynomials, and furthermore, the approximated probabilities might be negative. We solve this problem by employing the first quantization representation to give an algorithm for computing the marginal probabilities of these experiments. We prove that when the overall noise rate is constant, the algorithm runs in time quasi-polynomial in the number of input photons NNN and accuracy. When the overall noise rate scales as 1−x1γ1-x_1^γ1−x1γ​ for constant x1x_1x1​ and γ=Ω(log⁡N)γ=Ω(\log N)γ=Ω(logN), the running time becomes polynomial. Furthermore, we study noisy Boson Sampling with practically relevant noise models such as partial distinguishability and photon loss. We show that the same technique does not immediately apply in these settings, leaving open the possibility of a scalable demonstration of noisy quantum advantage for these noise models in certain parameter regimes.