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.

翻译：受实际硬件中噪声类型的启发，本文研究了在恒定噪声率下实际非单比特噪声源对随机量子电路输出分布的影响。我们证明，即使存在如去极化信道等单比特噪声源，在组合噪声信道作用下，输出分布在任何深度都不会趋近于最大熵分布。为证明这一点，我们论证了此类电路的输出分布永远不会达到反集中$\unicode{x2014}$即分布永远不会过于"平坦"$\unicode{x2014}$无论电路深度如何。这与无噪声随机量子电路或仅含单比特噪声的电路行为形成鲜明对比——后者在足够大的深度下均会呈现反集中现象。作为推论，我们的结果对含噪随机电路采样的难易性具有重要的算法意义，因为反集中特性正是当前最先进的经典难解性与易解性结果所共同依赖的关键性质。