Symmetry-informed transferability of optimal parameters in the Quantum Approximate Optimization Algorithm

TL;DR

This paper investigates how symmetries in the optimization landscape of the Quantum Approximate Optimization Algorithm (QAOA) can be used to transfer optimal parameters across different problem instances, improving the efficiency of variational quantum algorithms.

Contribution

It identifies symmetry properties in QAOA landscapes, defines transferable domains for parameters, and extends these findings to broader optimization problems and algorithms.

Findings

Symmetries in QAOA landscapes explain multiple optimal parameter sets.

Not all optimal parameters are transferable between instances.

Transferable domains enable efficient parameter initialization across problems.

Abstract

One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem symmetries and typical optimal parameters as initial points if they concentrate. In this article, we consider typical values of optimal parameters of the quantum approximate optimization algorithm for the MaxCut problem with d-regular tree subgraphs and reuse them in different graph instances. We prove symmetries in the optimization landscape of several kinds of weighted and unweighted graphs, which explains the existence of multiple sets of optimal parameters. However, we observe that not all optimal sets can be successfully transferred between problem instances. We find specific transferable domains in the search space and show how to translate an arbitrary set of optimal parameters into the adequate domain using the studied symmetries. Finally, we extend these results to general classical optimization problems described by Ising Hamiltonians, the Hamiltonian variational ansatz for relevant physical models, and the recursive and multi-angle quantum approximate optimization algorithms.