Exploiting Symmetry Reduces the Cost of Training QAOA

TL;DR

This paper introduces a symmetry-based method to significantly speed up the evaluation of QAOA energy, making the algorithm more practical for larger problems by reducing computational costs through exploiting problem symmetries.

Contribution

The authors develop a general approach leveraging problem symmetries to accelerate QAOA energy evaluation, applicable beyond graph problems and useful for nonlocal QAOA variants.

Findings

Achieved median speedup of 4.06x on benchmark graphs.

Improved evaluation efficiency for 71.7% of tested graphs at p=1.

Applicable to large graphs with up to 10,000 nodes.

Abstract

A promising approach to the practical application of the Quantum Approximate Optimization Algorithm (QAOA) is finding QAOA parameters classically in simulation and sampling the solutions from QAOA with optimized parameters on a quantum computer. Doing so requires repeated evaluations of QAOA energy in simulation. We propose a novel approach for accelerating the evaluation of QAOA energy by leveraging the symmetry of the problem. We show a connection between classical symmetries of the objective function and the symmetries of the terms of the cost Hamiltonian with respect to the QAOA energy. We show how by considering only the terms that are not connected by symmetry, we can significantly reduce the cost of evaluating the QAOA energy. Our approach is general and applies to any known subgroup of symmetries and is not limited to graph problems. Our results are directly applicable to nonlocal QAOA generalization RQAOA. We outline how available fast graph automorphism solvers can be leveraged for computing the symmetries of the problem in practice. We implement the proposed approach on the MaxCut problem using a state-of-the-art tensor network simulator and a graph automorphism solver on a benchmark of 48 graphs with up to 10,000 nodes. Our approach provides an improvement for $p=1$ on $71.7\%$ of the graphs considered, with a median speedup of $4.06$, on a benchmark where $62.5\%$ of the graphs are known to be hard for automorphism solvers.