Robust feedback-based quantum optimization: analysis and design

The Feedback-based Algorithm for Quantum Optimization (FALQON) is a Lyapunov inspired quantum algorithm proposed to tackle combinatorial optimization problems. In this thesis, we examine the robustness of FALQON against coherent control errors, a class of multiplicative errors that affect the control input, and shot noise. We show that the algorithm is asymptotically robust with respect to systematic errors, and we derive robustness bounds for independent errors. We prove marginal stability in presence of shot noise. Additionally, we propose a robust version of FALQON which minimizes a regularized Lyapunov function, allowing the algorithm to reach the optimum even in conditions where standard FALQON fails. Finally, we generalize the Lyapunov-based approach to Quantum Machine Learning (QML) problems, providing a general theoretical foundation that can be implemented with a variety of circuit architectures. Our theoretical results are supported through simulations for medium-scale common problems. The results related to robustness are tested on a MaxCut problem, while the QML results are tested on simple regression and binary classification tasks.