Efficient Quantum Algorithms for Quantum Optimal Control
Efficient Quantum Algorithms for Quantum Optimal Control
复制标题
DOI：
10.48550/arxiv.2304.02613
复制
发表时间：
2023-04
期刊：
影响因子：
--
通讯作者：
Xiantao Li;C. Wang
中科院分区：
文献类型：
--
作者：
Xiantao Li;C. Wang
在本文中，我们提出了一种有效的量子算法，它比经典算法以指数级的速度解决量子最优控制问题。这个问题涉及找到在时间$T$时物理量最大化的控制变量，其中系统由一个时变Schr\ odinger方程控制。这种类型的控制问题也与机器学习有着复杂的关系。我们的算法是基于一个时变哈密顿模拟方法和一个快速梯度估计算法。我们还提供了一个全面的误差分析，以量化各个步骤的总误差，例如控制函数的有限维表示，Schr\ odinger方程的离散化，数值正交和优化。我们的量子算法需要容错的量子计算机。
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time $T$, where the system is governed by a time-dependent Schr\"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.