Binary Control Pulse Optimization for Quantum Systems

Xinyu Fei1, Lucas T. Brady2, Jeffrey Larson3, Sven Leyffer3, and Siqian Shen1

1Department of Industrial and Operations Engineering, University of Michigan at Ann Arbor
2Joint Center for Quantum Information and Computer Science, NIST/University of Maryland
3Mathematics and Computer Science Division, Argonne National Laboratory

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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.


This work develops optimization methods that improve the numerical
efficiency and solution quality when solving quantum binary control problems.
These methods can be used for manipulating quantum systems towards specific
quantum states or desired operations, and are of vital importance to various
quantum applications, including energy minimization and circuit compilation.

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Cited by

[1] Xinyu Fei, Lucas T. Brady, Jeffrey Larson, Sven Leyffer, and Siqian Shen, "Binary Control Pulse Optimization for Quantum Systems", Quantum 7, 892 (2023).

[2] Christiane P. Koch, Ugo Boscain, Tommaso Calarco, Gunther Dirr, Stefan Filipp, Steffen J. Glaser, Ronnie Kosloff, Simone Montangero, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm, "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", arXiv:2205.12110, (2022).

[3] Ojas Parekh, "Synergies Between Operations Research and Quantum Information Science", arXiv:2301.05554, (2023).

[4] Robert J. Banks, Dan E. Browne, and P. A. Warburton, "Rapid quantum approaches for combinatorial optimisation inspired by optimal state-transfer", arXiv:2301.06846, (2023).

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