Gaussian Noise Sensitivity and BosonSampling

TL;DR

This paper analyzes how noise affects BosonSampling, showing that noise causes the output distributions to become highly sensitive and challenging to simulate quantumly, unless noise is very low or fault-tolerant methods are used.

Contribution

It provides a detailed analysis of noise sensitivity in BosonSampling and demonstrates classical approximability of noisy permanents, challenging claims of quantum advantage.

Findings

Correlation between noisy and noiseless outcomes tends to zero with increasing noise.

Classical algorithms can efficiently approximate the noisy permanent when noise is constant.

Noise significantly impacts the feasibility of demonstrating quantum speedup with BosonSampling.

Abstract

We study the sensitivity to noise of |permanent(X)|^2 for random real and complex n x n Gaussian matrices X, and show that asymptotically the correlation between the noisy and noiseless outcomes tends to zero when the noise level is {\omega}(1)/n. This suggests that, under certain reasonable noise models, the probability distributions produced by noisy BosonSampling are very sensitive to noise. We also show that when the amount of noise is constant the noisy value of |permanent(X)|^2 can be approximated efficiently on a classical computer. These results seem to weaken the possibility of demonstrating quantum-speedup via BosonSampling without quantum fault-tolerance.