QAOA Parameter Transfer for Hypergraphs

TL;DR

This paper develops analytical rules for reweighting QAOA parameters to transfer solutions across hypergraphs with different localities, improving optimization efficiency for complex hypergraph problems.

Contribution

It introduces novel reweighting rules for QAOA parameters tailored to hypergraphs, including mixing terms, based on analytical derivations and numerical validation.

Findings

Reweighting rules improve QAOA performance on hypergraphs with locality ≤ 5.

Analytical derivations rely on cycle-free, low-depth assumptions.

Numerical results outperform previous methods that ignore mixing term reweighting.

Abstract

Variational Quantum Algorithms, including the Quantum Approximate Optimization Algorithm (QAOA), have shown promise in solving optimization problems but rely on costly variational loops that can themselves be hard optimization problems. Many methods have been proposed to mitigate this variational cost, with one of the most common being parameter transfer and concentration where variational parameters for one problem instance or for an average over problem instances can be used as a good set of parameters for another instance. Methods exist for reweighting these parameters based off graph degree and edge weights, but there has been little work on how to do this reweighting to handle higher locality problems where the graph structure turns into a hypergraph structure. In this paper, we analytically derive parameter reweighting rules to transfer parameters between different locality hypergraphs, resulting in a reweighting for the mixing terms in the Hamiltonian which have previously not been considered. These analytics rely on three cycle-free and low-circuit-depth assumptions, but numerics indicate that the results can be used even when these assumptions are not satisfied. The numerics obtain high quality results across a diverse set of hypergraphs with locality less than or equal to five, improving on previous relations that do not reweight the mixing terms.