Quantum computational advantage of noisy boson sampling with partially distinguishable photons

TL;DR

This paper analyzes how partial distinguishability noise affects the classical intractability of boson sampling, showing that a logarithmic number of distinguishable photons preserves quantum advantage.

Contribution

It identifies the noise threshold of partial distinguishability that maintains the classical intractability of boson sampling, advancing understanding of noisy quantum systems.

Findings

Boson sampling with O(log N) distinguishable photons remains classically intractable.

Provides complexity-theoretic evidence supporting quantum advantage under noise.

Facilitates near-term experimental demonstrations of quantum computational advantage.

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 the 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 $O(\log N)$ number of 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.