时间相关量子期望计算中的降维方法
Dimensional Reductions for the Computation of Time-Dependent Quantum Expectations
AI总结：
针对混合量子系统中Liouville-von Neumann方程的期望值计算，提出基于切比雪夫多项式的直接期望计算方法（DEC），通过迹公式与修正切比雪夫多项式展开实现高效降维，并在核自旋系统中验证其随系统维度扩展的优越性能。
摘要：
我们考虑用于混合量子系统中期望值评估的Liouville-von Neumann方程的降维技术。在核自旋动力学等应用中，模拟的主要目标是能够模拟尽可能多自旋的系统，因此拥有一个随粒子数扩展良好的高效方法非常重要。我们描述了文献中出现的几种现有方法，指出了它们特别是在大系统设置中的局限性。我们引入了一种基于切比雪夫多项式的直接期望计算方法（DEC），该方法基于迹公式的评估与修正切比雪夫多项式展开相结合。这种降维方法非常高效且不破坏任何信息。我们展示了该方案在核自旋系统中的实际应用，并与几种替代方案进行了比较，重点研究了各种方法随系统维度增加的性能。我们的方法可应用于自主量子问题，其中量子模拟的期望结果不是系统动力学的完整描述，而仅仅是某个给定可观测量的期望值。
英文摘要：
We consider dimensional reduction techniques for the Liouville-von Neumann equation for the evaluation of the expectation values in a mixed quantum system. In applications such as nuclear spin dynamics the main goal for simulations is being able to simulate a system with as many spins as possible, for this reason it is very important to have an efficient method that scales well with respect to particle numbers. We describe several existing methods that have appeared in the literature, pointing out their limitations particularly in the setting of large systems. We introduce a method for direct computation of expectations via Chebyshev polynomials (DEC) based on evaluation of a trace formula combined with expansion in modified Chebyshev polynomials. This reduction is highly efficient and does not destroy any information. We demonstrate the practical application of the scheme for a nuclear spin system and compare with several alternatives, focusing on the performance of the various methods with increasing system dimension. Our method may be applied to autonomous quantum problems where the desired outcome of quantum simulation, rather than being a full description of the system dynamics, is only the expectation value of some given observable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
