This report is concerned with the efficiency of numerical methods for simulating quantum spin systems, with the aim to implement an improved method for simulation of a time-dependent Hamiltonian that displays chirped pulses at a high frequency. Working in the density matrix formulation of quantum systems, we study evolution under the Liouville-von Neumann equation, presenting analysis of and benchmarking current numerical methods. The accuracy of existing techniques is assessed in the presence of chirped pulses. We also discuss the Magnus expansion and detail how a truncation of it is used to solve differential equations. The results of this work are implemented in the Python package MagPy to provide a better error-to-cost ratio than current approaches allow for time-dependent Hamiltonians.

翻译：本报告关注于模拟量子自旋系统的数值方法效率问题，旨在实现一种改进方法，用于模拟包含高频啁啾脉冲的含时哈密顿量。在量子系统的密度矩阵框架下，我们研究了刘维尔-冯·诺依曼方程所描述的演化过程，对现有数值方法进行了分析并建立了基准测试。评估了现有技术在啁啾脉冲存在时的准确性。同时讨论了马格努斯展开，并详细阐述了如何利用其截断项求解微分方程。本研究结果已在Python软件包MagPy中实现，相较于现有方法，它在处理含时哈密顿量时提供了更优的误差-成本比。