We construct a polynomial-time classical algorithm that samples from the output distribution of low-depth noisy Clifford circuits with any product-state inputs and final single-qubit measurements in any basis. This class of circuits includes Clifford-magic circuits and Conjugated-Clifford circuits, which are important candidates for demonstrating quantum advantage using non-universal gates. Additionally, our results generalize a simulation algorithm for IQP circuits [Rajakumar et. al, SODA'25] to the case of IQP circuits augmented with CNOT gates, which is another class of non-universal circuits that are relevant to current experiments. Importantly, our results do not require randomness assumptions over the circuit families considered (such as anticoncentration properties) and instead hold for \textit{every} circuit in each class. This allows us to place tight limitations on the robustness of these circuits to noise. In particular, we show that there is no quantum advantage at large depths with realistically noisy Clifford circuits, even with perfect magic state inputs, or IQP circuits with CNOT gates, even with arbitrary diagonal non-Clifford gates. The key insight behind the algorithm is that interspersed noise causes a decay of long-range entanglement, and at depths beyond a critical threshold, the noise builds up to an extent that most correlations can be classically simulated. To prove our results, we merge techniques from percolation theory with tools from Pauli path analysis.

翻译：我们构建了一种多项式时间经典算法，该算法能够对任意乘积态输入、任意基下最终单量子比特测量的低深度含噪声Clifford电路的输出分布进行采样。此类电路包括Clifford-魔幻电路和共轭Clifford电路，它们是利用非通用门展示量子优势的重要候选方案。此外，我们的结果将IQP电路的模拟算法[Rajakumar等人，SODA'25]推广到用CNOT门增强的IQP电路情形，这是另一类与当前实验相关的非通用电路。重要的是，我们的结果不需要对所考虑电路族（如反集中特性）的随机性假设，而是对每个类别中的\textit{每一个}电路都成立。这使我们能够对这些电路的噪声鲁棒性施加严格限制。具体而言，我们证明：对于现实含噪声的Clifford电路，即使使用完美魔幻态输入，或在具有任意对角非Clifford门的情况下，对于用CNOT门增强的IQP电路，在大深度时均不存在量子优势。该算法背后的关键洞见在于：穿插的噪声会导致长程纠缠衰减，当深度超过临界阈值时，噪声累积到一定程度使得大多数关联都可以被经典模拟。为证明我们的结果，我们将渗流理论技术与泡利路径分析工具相结合。