Parameter Transfer for Quantum Approximate Optimization ofWeighted MaxCut

Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the objective landscape among different problem instances. However, we show that the more general weighted MaxCut problem has significantly modified objective landscapes, with a proliferation of poor local optima. Ourmain contribution is a simple rescaling scheme that overcomes these deleterious effects of weights. We show that for a given QAOA depth, a single typical vector of QAOA parameters can be successfully transferred to weighted MaxCut instances. This transfer leads to a median decrease in the approximation ratio of only 2.0 percentage points relative to a considerably more expensive direct optimization on a dataset of 34,701 instances with up to 20 nodes and multiple weight distributions. This decrease can be reduced to 1.2 percentage points at the cost of only 10 additional QAOA circuit evaluations with parameters sampled from a pretrained metadistribution, or the transferred parameters can be used as a starting point for a single local optimization run to obtain approximation ratios equivalent to those achieved by exhaustive optimization in 96.35% of our cases.

Automated summary

Researchers propose a simple rescaling scheme to overcome the difficulty of parameter optimization in the weighted MaxCut problem. They show that the empirical parameters can be successfully applied to weighted MaxCut instances, achieving approximation ratios equivalent to exhaustive optimization in 96.35% of cases among a dataset of nearly 34,701 instances.