Quantum-Assisted Barrier Sequential Quadratic Programming for Nonlinear Optimal Control

TL;DR

This paper introduces a quantum-assisted method for solving nonlinear optimal control problems more efficiently by integrating quantum algorithms into a classical barrier SQP framework, promising significant computational speedups.

Contribution

It presents a novel quantum-enhanced barrier SQP framework that improves the efficiency of solving constrained nonlinear optimal control problems, with detailed analysis of complexity and stability.

Findings

Quantum subroutine reduces computational complexity to polylogarithmic scale.

Framework achieves local stability and convergence with explicit error bounds.

Potential for quantum algorithms to significantly accelerate classical control optimization.

Abstract

We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated to efficiently solve the Schur complement step using block-encoding and Quantum Singular Value Transformation (QSVT) techniques. We formally analyze the time complexity and convergence behavior under the cumulative effect of quantum errors, establishing local input-to-state stability and convergence to a neighborhood of the stationary point, with explicit error bounds in terms of the barrier parameter and quantum solver accuracy. The proposed framework enables computational complexity to scale polylogarithmically with the system dimension demonstrating the potential of quantum algorithms to enhance classical optimization routines in nonlinear control applications.