Transferability of optimal QAOA parameters between random graphs

TL;DR

This paper investigates how optimal QAOA parameters can be transferred between different graph instances by analyzing local graph properties, enabling more efficient quantum optimization for combinatorial problems.

Contribution

It provides a theoretical framework linking parameter transferability to graph substructures, demonstrating successful transfer between different-sized random graphs.

Findings

Optimal parameters for small graphs can be used for larger graphs with minimal performance loss.

Transferability depends on local graph properties like subgraph types.

The approach accelerates quantum algorithms for specific classes of problems.

Abstract

The Quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. In a typical QAOA setup, a set of quantum circuit parameters is optimized to prepare a quantum state used to find the optimal solution of a combinatorial optimization problem. Several empirical observations about optimal parameter concentration effects for special QAOA MaxCut problem instances have been made in recent literature, however, a rigorous study of the subject is still lacking. We show that convergence of the optimal QAOA parameters around specific values and, consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on the local properties of the graphs, specifically the types of subgraphs (lightcones) from which the graphs are composed. We apply this approach to random regular and general random graphs. For example, we demonstrate how optimized parameters calculated for a 6-node random graph can be successfully used without modification as nearly optimal parameters for a 64-node random graph, with less than 1% reduction in approximation ratio as a result. This work presents a pathway to identifying classes of combinatorial optimization instances for which such variational quantum algorithms as QAOA can be substantially accelerated.