Binary Control Pulse Optimization for Quantum Systems

TL;DR

This paper develops and compares optimization algorithms for binary quantum control problems, enhancing solution quality and efficiency through novel regularizers and relaxation techniques, with demonstrated high-quality results in various quantum applications.

Contribution

It introduces a generic model with penalty and regularization, and develops new algorithms including ADMM and trust-region methods for binary quantum control optimization.

Findings

Algorithms achieve high-quality control results

Regularizers reduce control switches

Numerical studies validate effectiveness

Abstract

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 $L_2$-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.