



01465nas a2200169   4500008004100000245007200041210006900113260001400182520093400196100002301130700002001153700002501173700002101198700002101219700001801240856003701258       2021                        eng d00aTight bounds on the convergence of noisy random circuits to uniform0 aTight bounds on the convergence of noisy random circuits to unif  c12/1/20213 a<p>We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work.&nbsp;</p>1 aDeshpande, Abhinav1 aFefferman, Bill1 aGorshkov, Alexey, V.1 aGullans, Michael1 aNiroula, Pradeep1 aShtanko, Oles  uhttps://arxiv.org/abs/2112.00716