Robust feedback-based quantum optimization: analysis of coherent control errors

TL;DR

This paper analyzes the robustness of the FALQON quantum optimization algorithm against coherent control errors, demonstrating asymptotic robustness and proposing improvements to enhance error resilience.

Contribution

It provides the first theoretical analysis of FALQON's robustness to control errors and introduces a robust version that minimizes a regularized Lyapunov function.

Findings

FALQON is asymptotically robust to systematic errors

Derived bounds for independent coherent control errors

Proposed a robust FALQON variant with improved error mitigation

Abstract

The Feedback-based Algorithm for Quantum Optimization (FALQON) is a Lyapunov inspired quantum algorithm proposed to tackle combinatorial optimization problems. In this paper, we examine the robustness of FALQON against coherent control errors, a class of multiplicative errors that affect the control input. We show that the algorithm is asymptotically robust with respect to systematic errors, and we derive robustness bounds for independent errors. Finally, we propose a robust version of FALQON which minimizes a regularized Lyapunov function. Our theoretical results are supported through simulations.