A hybrid algorithm for quadratically constrained quadratic optimization problems

TL;DR

This paper introduces a hybrid quantum-classical algorithm for solving quadratically constrained quadratic programs (QCQPs), leveraging quantum amplitude encoding and classical optimization techniques to improve performance on problems like Max-Cut and power flow.

Contribution

It presents a novel variational quantum algorithm for QCQPs that scales efficiently with problem size and integrates classical primal-dual methods for handling constraints.

Findings

Outperforms classical algorithms on benchmark QCQP problems

Uses logarithmic qubit scaling with problem dimension

Demonstrates feasibility on current quantum devices

Abstract

Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables on the amplitude of a quantum state, the requirement of the qubit number scales logarithmically with the dimension of the variables, which makes our algorithm suitable for current quantum devices. Using the primal-dual interior-point method in classical optimization, we can deal with general quadratic constraints. Our numerical experiments on typical QCQP problems, including Max-Cut and optimal power flow problems, demonstrate a better performance of our hybrid algorithm over the classical counterparts.