Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem

Abstract

Today’s quantum computers are limited in their capabilities, e.g., the size of executable quantum circuits. The Quantum Approximate Optimization Algorithm (QAOA) addresses these limitations and is, therefore, a promising candidate for achieving a near-term quantum advantage. Warm-starting can further improve QAOA by utilizing classically pre-computed approximations to achieve better solutions at a small circuit depth. However, warm-starting requirements often depend on the quantum algorithm and problem at hand. Warm-started QAOA (WS-QAOA) requires developers to understand how to select approach-specific hyperparameter values that tune the embedding of classically pre-computed approximations. In this paper, we address the problem of hyperparameter selection in WS-QAOA for the maximum cut problem using the classical Goemans–Williamson algorithm for pre-computations. The contributions of this work are as follows: We implement and run a set of experiments to determine how different hyperparameter settings influence the solution quality. In particular, we (i) analyze how the regularization parameter that tunes the bias of the warm-started quantum algorithm towards the pre-computed solution can be selected and optimized, (ii) compare three distinct optimization strategies, and (iii) evaluate five objective functions for the classical optimization, two of which we introduce specifically for our scenario. The experimental results provide insights on efficient selection of the regularization parameter, optimization strategy, and objective function and, thus, support developers in setting up one of the central algorithms of contemporary and near-term quantum computing.

Keywords

• warm-starting
• QAOA
• maximum cut
• hyperparameter selection
• quantum optimization
• layer-wise optimization