量子自旋动力学随机模拟的重要抽样方案
Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
摘要：
量子相互作用系统动力学现象的数值模拟是一个非常困难的问题。虽然存在一些有前途的数值方法，但由于纠缠的增长或所谓的符号问题的存在，它们通常具有有限的适用性。在这项工作中，我们开发了一个重要的抽样方案的模拟量子自旋动力学，建立在最近的方法映射量子自旋系统的经典随机过程。重要性抽样方案是基于确定经典的轨迹，产生最大的贡献，一个给定的量子可观察。然后执行精确变换以优先采样接近主导轨迹的轨迹。我们证明，这种方法是能够减少的随机量的波动的时间增长，从而扩大了可访问的时间和系统大小的范围相比，直接采样。我们讨论了所提出的方法的优点和局限性，概述了进一步发展的方向。
英文摘要：
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.
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