Effect of non-unital noise on random circuit sampling

• URL: http://arxiv.org/abs/2306.16659v1
• Date: Thu, 29 Jun 2023 03:39:59 GMT
• Title: Effect of non-unital noise on random circuit sampling
• Authors: Bill Fefferman, Soumik Ghosh, Michael Gullans, Kohdai Kuroiwa, and Kunal Sharma
• Abstract summary: 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. This is stark contrast to the behavior of noiseless quantum circuits or those with only unit depths.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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