Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm

TL;DR

This paper explores unsupervised machine learning methods to determine optimal parameters for the Quantum Approximate Optimization Algorithm, reducing quantum circuit calls while maintaining high solution quality for combinatorial problems.

Contribution

It introduces unsupervised clustering strategies for setting QAOA parameters based on instance features and autoencoder outputs, avoiding extensive optimization.

Findings

Achieves median approximation ratio of 0.94 on MaxCut instances

Reduces quantum circuit calls compared to traditional optimization

Performs well up to QAOA depth 3 with limited parameters

Abstract

As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of the quantum circuit output. One of these algorithms, the Quantum Approximate Optimization Algorithm stands out as a promising approach to tackling combinatorial problems. However, finding the appropriate parameters is a difficult task. Although QAOA exhibits concentration properties, they can depend on instances characteristics that may not be easy to identify, but may nonetheless offer useful information to find good parameters. In this work, we study unsupervised Machine Learning approaches for setting these parameters without optimization. We perform clustering with the angle values but also instances encodings (using instance features or the output of a variational graph autoencoder), and compare different approaches. These angle-finding strategies can be used to reduce calls to quantum circuits when leveraging QAOA as a subroutine. We showcase them within Recursive-QAOA up to depth $3$ where the number of QAOA parameters used per iteration is limited to $3$, achieving a median approximation ratio of $0.94$ for MaxCut over $200$ Erd\H{o}s-R\'{e}nyi graphs. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.