Subgradient Method using Quantum Annealing for Inequality-Constrained Binary Optimization Problems

TL;DR

This paper explores applying the Ohzeki method, using quantum annealing, to inequality-constrained binary optimization problems, demonstrating how constraints can be incorporated into the objective function for quantum solvers.

Contribution

It extends the Ohzeki method to inequality constraints, enabling quantum annealing to handle a broader class of constrained optimization problems.

Findings

Inequality constraints can be relaxed into the objective function similarly to equality constraints.

The method is evaluated on the quadratic knapsack problem.

Performance results demonstrate the effectiveness of the approach.

Abstract

Quantum annealing is a generic solver for combinatorial optimization problems that utilizes quantum fluctuations. Recently, there has been extensive research applying quantum annealers, which are hardware implementations of quantum annealing. Since quantum annealers can only handle quadratic unconstrained binary optimization problems, to solve constrained combinatorial optimization problems using quantum annealers, the constraints must be incorporated into the objective function. One such technique is the Ohzeki method, which employs a Hubbard-Stratonovich transformation to relax equality constraints, and its effectiveness for large-scale problems has been demonstrated numerically. This study applies the Ohzeki method to combinatorial optimization problems with inequality constraints. We show that inequality constraints can be relaxed into a similar objective function through statistical mechanics calculations similar to those for equality constraints. In addition, we evaluate the performance of this method in a typical inequality-constrained combinatorial optimization problem, the quadratic knapsack problem.