Binary Quantum Control Optimization with Uncertain Hamiltonians

Xinyu Fei (), Lucas T. Brady (), Jeffrey Larson (), Sven Leyffer () and Siqian Shen ()
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Xinyu Fei: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109
Lucas T. Brady: KBR @ NASA Ames Quantum Artificial Intelligence Laboratory, Mountain View, California 94043
Jeffrey Larson: Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439
Sven Leyffer: Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439
Siqian Shen: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109

INFORMS Journal on Computing, 2025, vol. 37, issue 1, 86-106

Abstract: Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a discretized binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical simulations on various sized problem instances based on two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. We demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared with the controls of a deterministic model.

Keywords: quantum optimal control; stochastic optimization; conditional value-at-risk (CVaR); gradient-based algorithms (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:37:y:2025:i:1:p:86-106

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