We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to circuits with nearest-neighbor gates on an $O(1)$-D architecture with depolarizing noise after each gate. Importantly, we assume that the circuit does not contain qubit resets or mid-circuit measurements. 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 can be extended 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, these results do not require randomness assumptions over the circuit families considered (such as anticoncentration properties) and instead hold for every circuit in each class as long as the depth is above a constant threshold. This allows us to rule out the possibility of fault-tolerance in these circuit models. As a key technical step, we prove that interspersed noise causes a decay of long-range entanglement at depths beyond a critical threshold. To prove our results, we merge techniques from percolation theory and Pauli path analysis.

翻译：我们构建了一种多项式时间经典算法，该算法能够对具有任意乘积态输入和任意基下单量子比特测量的噪声几何局域Clifford电路的输出分布进行采样。我们的结果适用于在$O(1)$维架构上具有最近邻门控、且每个门后存在去极化噪声的电路。重要的是，我们假设电路中不包含量子比特重置或中途测量。这类电路包括Clifford-magic电路和共轭Clifford电路，它们是利用非通用门控展示量子优势的重要候选方案。此外，我们的结果可以扩展到由CNOT门增强的IQP电路，这是另一类与当前实验相关的非通用电路。关键的是，这些结果并不需要对所考虑的电路族（如反集中特性）进行随机性假设，而是只要深度超过一个常数阈值，对每个类别中的每个电路都成立。这使我们能够排除这些电路模型中存在容错性的可能性。作为一个关键的技术步骤，我们证明了穿插的噪声会导致深度超过临界阈值时，长程纠缠发生衰减。为了证明我们的结果，我们融合了渗流理论和泡利路径分析的技术。