The Better Solution Probability Metric: Optimizing QAOA to Outperform its Warm-Start Solution

TL;DR

This paper investigates Warm-Start QAOA for Max-Cut problems, introducing the Better Solution Probability metric to optimize parameters, leading to solutions outperforming classical warm-start solutions at certain tilt angles.

Contribution

It proposes the BSP metric for parameter optimization in Warm-Start QAOA, enabling the discovery of better solutions than classical warm-starts at specific tilt angles.

Findings

Warm-Start QAOA outperforms theoretical lower bounds on approximation ratios.

BSP-optimized QAOA finds solutions better than classical warm-start solutions.

Non-trivial tilt angles yield solutions surpassing classical warm-start performance.

Abstract

This paper presents a numerical simulation investigation of the Warm-Start Quantum Approximate Optimization Algorithm (QAOA) as proposed by Tate et al. [1], focusing on its application to 3-regular Max-Cut problems. Our study demonstrates that Warm-Start QAOA consistently outperforms theoretical lower bounds on approximation ratios across various tilt angles, highlighting its potential in practical scenarios beyond worst-case predictions. Despite these improvements, Warm-Start QAOA with traditional parameters optimized for expectation value does not exceed the performance of the initial classical solution. To address this, we introduce an alternative parameter optimization objective, the Better Solution Probability (BSP) metric. Our results show that BSP-optimized Warm-Start QAOA identifies solutions at non-trivial tilt angles that are better than even the best classically found warm-start solutions with non-vanishing probabilities. These findings underscore the importance of both theoretical and empirical analyses in refining QAOA and exploring its potential for quantum advantage.