Lyapunov control-inspired strategies for quantum combinatorial optimization

TL;DR

This paper explores Lyapunov control-inspired strategies for quantum optimization that eliminate the need for classical parameter tuning in QAOA, using feedback from measurements to improve solutions monotonically.

Contribution

It introduces a measurement-based, feedback-driven quantum optimization method that does not require classical optimization, enhancing efficiency and potentially improving near-term quantum applications.

Findings

Strategies effectively optimize MaxCut problems.

Performance comparable to or better than QAOA in simulations.

Robustness demonstrated under measurement noise.

Abstract

The prospect of using quantum computers to solve combinatorial optimization problems via the quantum approximate optimization algorithm (QAOA) has attracted considerable interest in recent years. However, a key limitation associated with QAOA is the need to classically optimize over a set of quantum circuit parameters. This classical optimization can have significant associated costs and challenges. Here, we provide an expanded description of Lyapunov control-inspired strategies for quantum optimization, as presented in [Magann et al., Phys. Rev. Lett. 129, 250502 (2022)], that do not require any classical optimization effort. Instead, these strategies utilize feedback from qubit measurements to assign values to the quantum circuit parameters in a deterministic manner, such that the combinatorial optimization problem solution improves monotonically with the quantum circuit depth. Numerical analyses are presented that investigate the utility of these strategies towards MaxCut on weighted and unweighted 3-regular graphs, both in ideal implementations and also in the presence of measurement noise. We also discuss how how these strategies compare with QAOA, how they may be used to seed QAOA optimizations in order to improve performance for near-term applications, and explore connections to quantum annealing.