用于多量子比特最优控制中高效梯度评估的解析级数展开
Analytical Series Expansion for Efficient Gradient Evaluation in Multi-Qubit Optimal Control
浏览论文内容
中文总结 AI 辅助
本文提出一种基于第一性原理的量子最优控制梯度计算统一框架，通过级数展开减少矩阵指数计算量，在GHZ态制备任务中较GOAT方法实现一个数量级以上的加速，适用于多量子比特平台的局域相互作用系统。
中文摘要 AI 辅助
基于梯度的量子最优控制方法对量子动力学进行开环优化时，需计算时间序传播子及其梯度。本文从第一性原理推导任意通用脉冲参数化下基于梯度的量子最优控制的统一框架，针对幺正传播子情况，推导包含时间无关对易子和时间相关系数的级数展开，大幅减少计算梯度所需的矩阵指数数量。该展开揭示了传播子导数与海森堡绘景中算子演化的关联，尤其适用于具有局域相互作用的量子系统最优控制任务模拟，这是大型多量子比特平台的常见场景。我们将该级数的计算成本与解析控制的梯度优化（GOAT）方法对比，以GHZ态制备问题为例，在量子比特阶梯和链结构中展示出一个数量级以上的加速效果。
英文摘要
Gradient-based quantum optimal control and the theory of operator evolution are rarely discussed together. In this Letter, we bridge this gap by showing that the gradient of the time-evolved propagator involves the Heisenberg evolution of local operators. We present a unifying framework by deriving from first principles the formal solution for the gradient under an arbitrary pulse parameterization, and show that the same construction extends to derivatives of any order. We obtain a series of nested, time-independent commutators weighted by time-dependent scalar coefficients. The commutators are thus computed once, and each optimization step only updates the scalars. The method is particularly suited for simulating optimal control tasks in quantum systems with local interactions, which is a common situation in large multi-qubit platforms. In this setting, light-cone arguments and sparse-Pauli truncation heuristics may be used to keep the number of relevant terms in the series small. We compare the computational cost required for the series with the Gradient Optimization of Analytic conTrols (GOAT) method, and, focusing on the problem of preparation of a GHZ state, demonstrate more than an order of magnitude speedup for a qubit ladder and a chain geometry.
发表机构
- Institute for Quantum Computing Analytics (PGI-12) Forschungszentrum Jülich（于利希研究中心量子计算分析研究所）
- Theoretical Physics, Universität des Saarlandes（萨尔兰州立大学理论物理系）
机构由 AI 辅助整理，请以论文原文为准。
