We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the computational basis). Our approach is based upon the intuition that noise exponentially damps non-local correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by only keeping track of the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasi-polynomial time, so long as the distribution anti-concentrates. A number of practical implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: any quantum circuit for which error mitigation is efficient must be classically simulable.

翻译：我们提出了一种针对含噪量子线路的多项式时间经典算法。该算法能够计算任意线路中任意可观测量在输入态系综（例如计算基）上的期望值，且平均误差较小。我们的方法基于以下直观理解：噪声会以指数方式抑制非局域关联相对于局域关联的影响。这使得我们能够仅通过追踪局域量子信息的动力学来经典地模拟含噪量子线路。只要输出分布满足反集中条件，我们的算法还能在拟多项式时间内从线路的输出分布中进行采样。本文讨论了若干实际意义，包括噪声缓解策略有效性的一个基本限制：任何能够高效进行误差缓解的量子线路，必定是经典可模拟的。