On computational complexity and average-case hardness of shallow-depth boson sampling

TL;DR

This paper investigates the computational complexity of shallow-depth boson sampling, demonstrating average-case hardness in logarithmic-depth regimes, which could enable more noise-tolerant quantum advantage demonstrations.

Contribution

It establishes average-case hardness for logarithmic-depth boson sampling, advancing understanding of its classical intractability under realistic, noisy conditions.

Findings

Average-case hardness for logarithmic-depth boson sampling

Hardness results for lossy and Gaussian variants

Implications for noise-tolerant quantum advantage

Abstract

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 under various noise models that can efficiently simulate boson sampling as noise rates increase with circuit depth. To address this issue particularly related to circuit depth, we explore the viability of achieving quantum computational advantage through boson sampling with shallow-depth linear optical circuits. Specifically, 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 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.