In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full matrix. We implement this algorithm using an in-house simulator and show that the low-rank algorithm speeds up simulations by more than two orders of magnitude over existing implementations of full-rank simulators, and with negligible error in the noise effect and final observables. Finally, we demonstrate the utility of the low-rank method as applied to representative problems of interest by using the algorithm to speed up noisy simulations of Grover’s search algorithm and quantum chemistry solvers.

在这项工作中，我们提出了一种有效的秩压缩方法，用于在嘈杂的量子电路中对Kraus去相干通道进行经典模拟。通过在每个模拟步骤中基于密度矩阵的先验本征值对密度矩阵进行迭代压缩，无需存储，操作或对角化整个矩阵，即可实现近似值。我们使用内部模拟器来实现该算法，并表明低秩算法比全秩模拟器的现有实现方式将仿真的速度提高了两个数量级以上，并且噪声影响和最终可观察到的误差可忽略不计。最后，我们通过使用该算法来加快Grover搜索算法和量子化学求解器的嘈杂仿真，证明了低秩方法在感兴趣的代表性问题上的实用性。