Binary Control Pulse Optimization for Quantum Systems
Binary Control Pulse Optimization for Quantum Systems
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DOI：
10.22331/q-2023-01-04-892
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发表时间：
2022-04
期刊：
影响因子：
6.4
通讯作者：
Xinyu Fei;L. Brady;Jeffrey Larson;S. Leyffer;Siqian Shen
中科院分区：
文献类型：
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作者：
Xinyu Fei;L. Brady;Jeffrey Larson;S. Leyffer;Siqian Shen
量子控制的目的是操纵量子系统达到特定的量子状态或所需的操作。设计高精度和高效的控制步骤对于各种量子应用至关重要，包括能量最小化和电路编译。本文以离散二元量子控制问题为研究对象，采用不同的优化算法和技术来提高计算效率和求解质量。具体地说，我们开发了一个通用模型，并以多种方式对其进行了扩展。我们引入了一个平方的L2惩罚函数来处理额外的边约束，以对诸如允许至多一个控件为活动的需求进行建模。我们引入了总变分(TV)正则化来减少控制中的开关数量。我们改进了流行的梯度上升脉冲工程(GRPE)算法，提出了一种新的交替方向乘子法(ADMM)算法来解决惩罚模型的连续松弛问题，然后应用舍入技术获得二元控制解。我们提出了一种改进的信赖域方法来进一步改进解。我们的算法可以获得高质量的控制结果，通过对各种量子控制实例的数值研究证明了这一点。
Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared L2-penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples.