Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
中文速览 本文提出了一种高效且可高度并行化的经典算法，用于模拟受任意单量子比特噪声影响的n比特量子线路。该算法基于张量网络，其核心思想是将含噪量子系统的状态表示为一组矩阵乘积态（MPS）的系综。关键创新在于，对于作用在任意纯态上的每个单比特噪声过程，算法会选择一种特定的“展开”（即Kraus分解），这种展开能最小化该噪声比特与系统其余部分之间的平均纠缠（即纠缠形成熵）。通过将这个n比特问题映射到一个等效的两比特问题，作者为这种最优展开提供了封闭形式的解析解，从而避免了启发式优化并适用于任何单比特噪声模型。这种方法使得在给定的精度和噪声水平下，能够用更紧凑的MPS来表示量子态。此外，该工作还为这类基于展开的模拟器提供了严格的误差上限，并证明了先前工作中使用的固定展开策略，在其适用的特定噪声模型下，等价于本文方法在随机态上的特例。 English Research Briefing Research Briefing: Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings 1. The Core Contribution This paper introduces a highly general and efficient tensor-network-based algorithm for the classical simulation of one-dimensional noisy quantum circuits. The central thesis is that the simulation’s efficiency can be dramatically improved by strategically choosing how to represent the effect of noise. The primary contribution is a method to select a state-dependent, locally entanglement-optimal unraveling for any single-qubit noise channel. This is achieved by finding the specific Kraus decomposition that minimizes the average von Neumann entanglement (achieving the entanglement of formation) between the noisy qubit and the rest of the system. This approach provides a provably optimal local strategy for reducing the entanglement in the underlying Matrix Product State (MPS) representation, thereby lowering computational cost and improving accuracy for a given bond dimension, and importantly, comes with rigorous, a posteriori error guarantees. ...