通过经典搜索优化马尔可夫开放量子系统的Trotter-Suzuki模拟
Optimising Trotter-Suzuki Simulations of Markovian Open Quantum Systems via Classical Search
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中文总结 AI 辅助
该研究针对马尔可夫开放量子系统的Trotter-Suzuki模拟，推导了TS-PF的解析界，提出结合二分搜索与diamond范数估计的经典算法，通过数值实验验证二阶随机TS-PF资源效率更高，优化了模拟所需的Trotter步数。
中文摘要 AI 辅助
在数字量子计算机上模拟开放量子系统时，通常需要使用Trotter-Suzuki（TS）乘积公式（PF）来近似系统的时间演化。准确估计所需的Trotter步数（进而决定总门数）对于最小化这些方法的计算成本至关重要。基于已有的理论保证，我们推导了一阶和二阶确定性及随机TS-PF的解析界，直接将Trotter步数与模型参数、演化时间和精度关联起来，这些界能为每种方法提供具体的资源估计。随后，我们提出一种计算高效的经典算法，该算法利用单个Liouvillian项的diamond范数估计和二分搜索，可大幅降低达到目标精度所需的Trotter步数。我们在两个典型模型上的数值结果——带边界驱动和局域退相的XX自旋链，以及横场伊辛模型——显示，理论（解析）界通常过于保守，而经验（优化）界在相同精度下能得到显著更少的Trotter步数。在所研究的方法中，二阶随机TS-PF通常实现最低的资源需求，尤其对于更大的系统。这些发现强调了经验界策略在实现马尔可夫开放量子系统更资源高效模拟中的重要性。
英文摘要
Simulating an open quantum system on a digital quantum computer often involves the use of Trotter-Suzuki (TS) Product Formulas (PF) to approximate the system's time evolution. Precise estimates for the required number of Trotter steps (and hence the overall gate count) can be crucial for minimising the computational cost of these methods. Building on established theoretical guarantees, we derive analytic bounds for the First- and Second-Order Deterministic and Randomised TS-PF, directly relating the number of Trotter steps to the model parameters, evolution time and precision. These bounds enable concrete resource estimation for each method. We then present a computationally efficient classical algorithm that uses diamond norm estimates of individual Liouvillian terms and a binary search to significantly reduce the Trotter steps required for a target precision. Our numerical results on two prototypical models - an XX-Spin Chain with boundary driving and local dephasing, and a Transverse-Field Ising Model - show that the theoretical (analytic) bounds are often overly conservative, whereas the empirical (optimised) bounds yield a significantly smaller number of Trotter steps for the same precision. Among the methods investigated, the Second-Order Randomised TS-PF typically achieves the lowest resource demands, especially for larger systems. These findings emphasise the significance of empirical bounding strategies in achieving more resource-efficient simulations of Markovian open quantum systems.
