Automatic Depth Optimization for Quantum Approximate Optimization Algorithm

TL;DR

This paper introduces an automatic method based on proximal gradient descent to optimize the control depth of QAOA, reducing quantum gate count and enhancing performance on NISQ devices.

Contribution

It presents a novel automatic control depth selection algorithm for QAOA with theoretical convergence guarantees, improving over empirical or random search methods.

Findings

Control depth can be significantly reduced during optimization.

The algorithm achieves sufficient accuracy with fewer parameters.

Reduction in control depth decreases quantum circuit complexity.

Abstract

Quantum Approximate Optimization Algorithm (QAOA) is a hybrid algorithm whose control parameters are classically optimized. In addition to the variational parameters, the right choice of hyperparameter is crucial for improving the performance of any optimization model. Control depth, or the number of variational parameters, is considered as the most important hyperparameter for QAOA. In this paper we investigate the control depth selection with an automatic algorithm based on proximal gradient descent. The performances of the automatic algorithm are demonstrated on 7-node and 10-node Max-Cut problems, which show that the control depth can be significantly reduced during the iteration while achieving an sufficient level of optimization accuracy. With theoretical convergence guarantee, the proposed algorithm can be used as an efficient tool for choosing the appropriate control depth as a replacement of random search or empirical rules. Moreover, the reduction of control depth will induce a significant reduction in the number of quantum gates in circuit, which improves the applicability of QAOA on Noisy Intermediate-scale Quantum (NISQ) devices.