The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or the presence of the so-called sign problem. In this work, we develop an importance sampling scheme for the simulation of quantum spin dynamics, building on a recent approach mapping quantum spin systems to classical stochastic processes. The importance sampling scheme is based on identifying the classical trajectory that yields the largest contribution to a given quantum observable. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the stochastic quantities, thus extending the range of accessible times and system sizes compared to direct sampling. We discuss advantages and limitations of the proposed approach, outlining directions for further developments.

中文翻译：

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量子自旋动力学随机模拟的重要性采样方案

相互作用量子系统中动力学现象的数值模拟是一个众所周知的难题。尽管存在许多有前途的数值方法，但由于纠缠的增长或所谓的符号问题的存在，它们的适用性通常有限。在这项工作中，我们基于最近将量子自旋系统映射到经典随机过程的方法，开发了一种用于模拟量子自旋动力学的重要采样方案。重要性采样方案基于识别对给定量子可观察量产生最大贡献的经典轨迹。然后执行精确转换以优先采样接近主导轨迹的轨迹。我们证明，与直接采样相比，这种方法能够减少随机量波动的时间增长，从而扩展可访问时间和系统大小的范围。我们讨论了所提出方法的优点和局限性，概述了进一步发展的方向。