Solving constrained quadratic binary problems via quantum adiabatic evolution

TL;DR

This paper introduces a quantum adiabatic evolution method for efficiently solving constrained binary quadratic programming problems by addressing inequality constraints through a Lagrangian dual approach within a branch-and-bound framework.

Contribution

It presents a novel quantum adiabatic approach for handling inequality constraints in constrained binary quadratic problems, extending previous methods that focused on unconstrained cases.

Findings

Developed a method for solving the Lagrangian dual of CBQP problems.

Integrated the dual approach within a branch-and-bound framework.

Provides a foundation for quantum algorithms addressing inequality constraints.

Abstract

Quantum adiabatic evolution is perceived as useful for binary quadratic programming problems that are a priori unconstrained. For constrained problems, it is a common practice to relax linear equality constraints as penalty terms in the objective function. However, there has not yet been proposed a method for efficiently dealing with inequality constraints using the quantum adiabatic approach. In this paper, we give a method for solving the Lagrangian dual of a binary quadratic programming (BQP) problem in the presence of inequality constraints and employ this procedure within a branch-and-bound framework for constrained BQP (CBQP) problems.