Parameter optimization comparison in QAOA using Stochastic Hill Climbing with Random Re-starts and Local Search with entangled and non-entangled mixing operators

TL;DR

This paper compares stochastic hill climbing with random restarts to local search in QAOA, finding SHC-RR generally outperforms LS and that entanglement stages in mixing operators significantly influence performance.

Contribution

It introduces a comprehensive comparison of SHC-RR and LS in QAOA across various models, highlighting the impact of entanglement in mixing operators on optimization outcomes.

Findings

SHC-RR outperforms LS in QAOA optimization.

Entanglement stages in mixing operators significantly affect performance.

Performance varies depending on problem type and mixing operator configuration.

Abstract

This study investigates the efficacy of Stochastic Hill Climbing with Random Restarts (SHC-RR) compared to Local Search (LS) strategies within the Quantum Approximate Optimization Algorithm (QAOA) framework across various problem models. Employing uniform parameter settings, including the number of restarts and SHC steps, we analyze LS with two distinct perturbation operations: multiplication and summation. Our comparative analysis encompasses multiple versions of max-cut and random Ising model (RI) problems, utilizing QAOA models with depths ranging from $1L$ to $3L$. These models incorporate diverse mixing operator configurations, which integrate $RX$ and $RY$ gates, and explore the effects of an entanglement stage within the mixing operator. Our results consistently show that SHC-RR outperforms LS approaches, showcasing superior efficacy despite its ostensibly simpler optimization mechanism. Furthermore, we observe that the inclusion of entanglement stages within mixing operators significantly impacts model performance, either enhancing or diminishing results depending on the specific problem context.