While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in $n^{\rm{polylog}(n)}$ time for simulating quantum circuits under local depolarizing noise, thereby ruling out their quantum advantage in these settings. Our algorithm leverages a property called approximate Markovianity to sequentially sample from the measurement outcome distribution of noisy circuits. We establish approximate Markovianity in a broad range of circuits: (1) we prove that it holds for any circuit when the noise rate exceeds a constant threshold, and (2) we provide strong analytical and numerical evidence that it holds for random quantum circuits subject to any constant noise rate. These regimes include previously known classically simulable cases as well as new ones, such as shallow random circuits without anticoncentration, where prior algorithms fail. Taken together, our results significantly extend the boundary of classical simulability and suggest that noise generically enforces approximate Markovianity and classical simulability, thereby highlighting the limitation of noisy quantum circuits in demonstrating quantum advantage.

翻译：尽管量子计算能够完成经典计算难以处理的任务，但在缺乏容错能力的情况下，噪声的存在可能会破坏这一优势。本文提出一种经典算法，可在$n^{\rm{polylog}(n)}$时间内模拟局部去极化噪声下的量子线路，从而在这些场景中排除了其量子优势。该算法利用近似马尔可夫性这一特性，对含噪线路的测量结果分布进行顺序采样。我们在广泛的线路类别中建立了近似马尔可夫性：(1) 证明当噪声率超过恒定阈值时，该性质对所有线路均成立；(2) 通过理论分析与数值模拟提供强有力证据，表明该性质对任何恒定噪声率下的随机量子线路均成立。这些研究范围既包含先前已知的经典可模拟情形，也涵盖如缺乏反集中性的浅层随机线路等新场景——而现有算法在这些场景中均告失效。综合而言，我们的研究显著拓展了经典可模拟性的边界，并表明噪声通常会导致近似马尔可夫性与经典可模拟性，这凸显了含噪量子线路在证明量子优势方面存在的局限性。