A quantum approach for optimal control

• URL: http://arxiv.org/abs/2407.02864v3
• Date: Tue, 13 May 2025 10:20:57 GMT
• Title: A quantum approach for optimal control
• Authors: Hirmay Sandesara, Alok Shukla, Prakash Vedula,
• Abstract summary: We propose a novel variational quantum approach for solving a class of nonlinear optimal control problems.<n>Our approach integrates Dirac's canonical quantization of dynamical systems with the solution of the ground state of a non-Hermitian Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we propose a novel variational quantum approach for solving a class of nonlinear optimal control problems. Our approach integrates Dirac's canonical quantization of dynamical systems with the solution of the ground state of the resulting non-Hermitian Hamiltonian via a variational quantum eigensolver (VQE). We introduce a new perspective on the Dirac bracket formulation for generalized Hamiltonian dynamics in the presence of constraints, providing a clear motivation and illustrative examples. Additionally, we explore the structural properties of Dirac brackets within the context of multidimensional constrained optimization problems. Our approach for solving a class of nonlinear optimal control problems employs a VQE-based approach to determine the eigenstate and corresponding eigenvalue associated with the ground state energy of a non-Hermitian Hamiltonian. Assuming access to an ideal VQE, our formulation demonstrates excellent results, as evidenced by selected computational examples. Furthermore, our method performs well when combined with a VQE-based approach for non-Hermitian Hamiltonian systems. Our VQE-based formulation effectively addresses challenges associated with a wide range of optimal control problems, particularly in high-dimensional scenarios. Compared to standard classical approaches, our quantum-based method shows significant promise and offers a compelling alternative for tackling complex, high-dimensional optimization challenges.

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