Exploiting In-Constraint Energy in Constrained Variational Quantum Optimization

TL;DR

This paper introduces a novel quantum optimization method that enhances solution quality for constrained problems by leveraging in-constraint energy and probability bounds, implemented in a user-friendly Python package.

Contribution

The authors propose a new approach that uses in-constraint energy and probability bounds to improve constrained quantum optimization, avoiding complex circuit encoding.

Findings

Significant improvement in solution quality over penalized energy methods

Effective implementation in Qiskit-based Python package

Applicable to simulators and quantum hardware

Abstract

A central challenge of applying near-term quantum optimization algorithms to industrially relevant problems is the need to incorporate complex constraints. In general, such constraints cannot be easily encoded in the circuit, and the quantum circuit measurement outcomes are not guaranteed to respect the constraints. Therefore, the optimization must trade off the in-constraint probability and the quality of the in-constraint solution by adding a penalty for constraint violation into the objective. We propose a new approach for solving constrained optimization problems with unconstrained, easy-to-implement quantum ansatze. Our method leverages the in-constraint energy as the objective and adds a lower-bound constraint on the in-constraint probability to the optimizer. We demonstrate significant gains in solution quality over directly optimizing the penalized energy. We implement our method in QVoice, a Python package that interfaces with Qiskit for quick prototyping in simulators and on quantum hardware.