用于高度振荡受控量子系统的菲隆方法
Filon Methods for Highly Oscillatory Controlled Quantum Systems
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中文总结 AI 辅助
研究针对量子系统高度振荡动力学限制标准数值方法效率的问题，将菲隆求积法改编为菲隆法和受控菲隆法，经实验验证能显著降低超导transmon量子比特系统模拟成本，受控菲隆法在模拟CNOT门动力学时效率最高。
中文摘要 AI 辅助
快速准确地对量子系统进行经典模拟是量子计算机设计与控制中的核心挑战，因其高度振荡动力学严重限制了标准数值方法的效率。为解决此问题，我们将用于振荡积分的菲隆求积法改编为两种数值方法，即菲隆法和受控菲隆法，用于求解具有高度振荡解的常微分方程线性系统。我们针对受控量子系统进行了高效实现的定制，受控菲隆法还考虑了控制脉冲的振荡结构。数值实验表明，这些方法通过减少达到给定精度所需的时间步数，显著降低了精确模拟超导transmon量子比特系统的计算成本，每时间步成本仅适度增加。对于CNOT门动力学的实际模拟，受控菲隆法在每个目标精度下都是测试中最有效的方法，比最佳埃尔米特方法效率高6倍，比同阶埃尔米特方法效率高500倍。
英文摘要
Fast and accurate classical simulation of quantum systems is a central challenge in the design and control of quantum computers, but the highly oscillatory dynamics of these systems severely limit the efficiency of standard numerical methods. To address this, we adapt Filon quadrature for oscillatory integrals into two numerical methods, called Filon and Controlled Filon, for solving linear systems of ODEs with highly oscillatory solutions. We tailor both methods for efficient implementation in controlled quantum systems, and the Controlled Filon method additionally accounts for the oscillatory structure of the control pulses. We show by numerical experiments that these methods significantly reduce the computational cost of accurately simulating systems of superconducting transmon qubits by decreasing the number of timesteps needed to reach a given level of precision, with only a modest increase in the cost per timestep. For a realistic simulation of the dynamics of a CNOT gate, the Controlled Filon method is the most efficient method tested at every target accuracy, outperforming the best Hermite method by up to 6x and the Hermite method of the same order by up to 500x.
