A quantum approach for optimal control

TL;DR

This paper introduces a quantum variational approach combining Dirac's quantization and VQE to solve complex nonlinear optimal control problems, especially in high-dimensional systems, showing promising results.

Contribution

It presents a novel quantum method integrating Dirac brackets with VQE for nonlinear optimal control, advancing quantum optimization techniques for constrained dynamical systems.

Findings

Effective in high-dimensional control problems

Performs well with non-Hermitian Hamiltonians

Shows promising results compared to classical methods

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.