Lyapunov-control-inspired strategies for quantum combinatorial optimization

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