Effect of non-unital noise on random circuit sampling

TL;DR

This paper investigates how realistic non-unital noise affects the output distribution of random quantum circuits, showing it prevents the distribution from becoming maximally entropic and impacts classical hardness assumptions.

Contribution

It demonstrates that non-unital noise prevents anticoncentration in random circuits, contrasting with noiseless or unital-noise cases, and explores implications for classical simulation complexity.

Findings

Output distribution never anticoncentrates under non-unital noise

Distribution remains non-maximally entropic at all depths

Implications for classical hardness and easiness of noisy sampling

Abstract

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 $\unicode{x2014}$ meaning it is never too "flat" $\unicode{x2014}$ 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.