Benchmarking Swarm Optimization Algorithms for Parameter Initialization in the Quantum Approximate Optimization Algorithm

TL;DR

This paper benchmarks various swarm optimization algorithms for tuning QAOA parameters, demonstrating their superior performance and stability over traditional optimizers in noisy and resource-limited quantum settings.

Contribution

It introduces and evaluates swarm-based optimization methods as effective tools for QAOA parameter tuning, especially under realistic noise conditions.

Findings

Swarm algorithms achieve lower approximation gaps than standard optimizers.

Swarm methods show more stable convergence across different noise regimes.

Population-based search effectively navigates the complex QAOA landscape.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a prominent variational algorithm for solving combinatorial optimization problems such as the Max Cut problem. A key challenge in QAOA is the efficient identification of variational parameters ({\gamma}, \{beta}) that yield high-quality solutions. In this work, we investigate swarm optimization methods as robust strategies for exploring the QAOA parameter space. We evaluate Particle Swarm Optimization (PSO), Fully Informed Particle Swarm Optimization (FIPSO), Quantum Particle Swarm Optimization (QPSO), and an Adam-assisted FIPSO variant on weighted MaxCut instances across multiple system sizes, circuit depths, and noise regimes, including shot noise. Our results show that these methods achieve lower approximation gaps and more stable convergence compared to standard optimizers such as Adam, COBYLA, and SPSA. In particular, we observe that swarm methods maintain superior performance under noisy and shot limited conditions. These findings suggest that population based search is effective for navigating the complex QAOA landscape and is a promising approach for parameter optimization in near-term quantum algorithms.