Quantum Approximate Optimization Algorithm Parameter Prediction Using a Convolutional Neural Network

TL;DR

This paper introduces a convolutional neural network model to predict QAOA parameters, enabling initialization and optimization strategies that improve solution quality for combinatorial problems like Max-Cut.

Contribution

The work presents a novel neural network approach to predict QAOA parameters, facilitating deeper circuit optimization with limited training data from shallower instances.

Findings

Achieved an average approximation ratio of 0.9759 for Max-Cut.

Successfully initialized depth 10 QAOA instances using parameters from shallower depths.

Repetitive application of the model enhances maximum expected value in QAOA solutions.

Abstract

The Quantum approximate optimization algorithm (QAOA) is a quantum-classical hybrid algorithm aiming to produce approximate solutions for combinatorial optimization problems. In the QAOA, the quantum part prepares a quantum parameterized state that encodes the solution, where the parameters are optimized by a classical optimizer. However, it is difficult to find optimal parameters when the quantum circuit becomes deeper. Hence, there is numerous active research on the performance and the optimization cost of QAOA. In this work, we build a convolutional neural network to predict parameters of depth QAOA instance by the parameters from the depth QAOA counterpart. We propose two strategies based on this model. First, we recurrently apply the model to generate a set of initial values for a certain depth QAOA. It successfully initiates depth 10 QAOA instances, whereas each model is only trained with the parameters from depths less than 6. Second, the model is applied repetitively until the maximum expected value is reached. An average approximation ratio of 0.9759 for Max-Cut over 264 Erd\H{o}s-R\'{e}nyi graphs is obtained, while the optimizer is only adopted for generating the first input of the model.