We give a polynomial time classical algorithm for sampling from the output distribution of a noisy random quantum circuit in the regime of anti-concentration to within inverse polynomial total variation distance. This gives strong evidence that, in the presence of a constant rate of noise per gate, random circuit sampling (RCS) cannot be the basis of a scalable experimental violation of the extended Church-Turing thesis. Our algorithm is not practical in its current form, and does not address finite-size RCS based quantum supremacy experiments.
@article{arxiv.2211.03999,
title = {A polynomial-time classical algorithm for noisy random circuit sampling},
author = {Dorit Aharonov and Xun Gao and Zeph Landau and Yunchao Liu and Umesh Vazirani},
journal= {arXiv preprint arXiv:2211.03999},
year = {2023}
}