A Subgradient Approach for Constrained Binary Optimization via Quantum Adiabatic Evolution

TL;DR

This paper introduces a subgradient method for constrained binary optimization that improves quantum annealing performance by effectively handling noise, demonstrated through experiments on the D-Wave 2X quantum annealer with the quadratic stable set problem.

Contribution

It proposes a novel subgradient approach for primal-dual optimization in quantum annealing, avoiding large penalties and enhancing success rates on noisy quantum hardware.

Findings

The subgradient method improves success rates on the D-Wave 2X.

It effectively handles noise without large penalty coefficients.

Experimental results show better performance compared to traditional penalty methods.

Abstract

An earlier work [18] proposes a method for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution using an outer approximation method. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.