



01506nas a2200157   4500008004100000245005800041210005700099260001400156520104400170100002001214700001801234700002101252700002001273700001801293856003701311       2023                        eng d00aEffect of non-unital noise on random circuit sampling0 aEffect of nonunital noise on random circuit sampling  c6/28/20233 a<p>In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates &mdash; meaning it is never too &quot;flat&quot; &mdash; regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.</p>1 aFefferman, Bill1 aGhosh, Soumik1 aGullans, Michael1 aKuroiwa, Kohdai1 aSharma, Kunal  uhttps://arxiv.org/abs/2306.16659