Quantum annealing with inequality constraints: the set cover problem

TL;DR

This paper introduces two innovative quantum annealing methods for solving the set cover problem with inequality constraints, demonstrating superior performance over traditional slack variable approaches on D-Wave quantum hardware.

Contribution

It presents the augmented Lagrangian and HUBO formulations for inequality constraints, expanding quantum annealing capabilities for constrained optimization problems.

Findings

Both methods outperform standard slack variable approach.

Augmented Lagrangian handles many constraints effectively.

HUBO performs slightly better but less scalable.

Abstract

This paper presents two novel approaches for solving the set cover problem (SCP) with multiple inequality constraints on quantum annealers. The first method uses the augmented Lagrangian approach to represent the constraints, while the second method employs a higher-order binary optimization (HUBO) formulation. Our experimental analysis demonstrate that both approaches outperform the standard approach with slack variables for solving problems with inequality constraints on D-Wave quantum annealers. The results show that the augmented Lagrangian method can be successfully used to implement a large number of inequality constraints, making it applicable to a wide range of constrained problems beyond the SCP. The HUBO formulation performs slightly better than the augmented Lagrangian method in solving the SCP, but it is less scalable in terms of embeddability in the quantum chip. These findings could impact the use of quantum annealers for solving constrained optimization problems.