Solving Inequality-Constrained Binary Optimization Problems on Quantum Annealer

TL;DR

This paper introduces a novel quantum annealing method for inequality-constrained binary optimization that avoids slack variables, enabling larger problem sizes and faster solutions compared to traditional approaches.

Contribution

The study presents an alternative approach using the alternating direction method of multipliers, improving scalability and efficiency in quantum annealing for constrained optimization.

Findings

Sampling mode yields highest accuracy.

Our method is faster than exact solvers on dense graphs.

Effective for quadratic knapsack problems.

Abstract

We propose a new method for solving binary optimization problems under inequality constraints using a quantum annealer. To deal with inequality constraints, we often use slack variables, as in previous approaches. When we use slack variables, we usually conduct a binary expansion, which requires numerous physical qubits. Therefore, the problem of the current quantum annealer is limited to a small scale. In this study, we employ the alternating direction method of multipliers. This approach allows us to deal with various types using constraints in the current quantum annealer without slack variables. To test the performance of our algorithm, we use quadratic knapsack problems (QKPs). We compared the accuracy obtained by our method with a simulated annealer and the optimization and sampling mode of a D-Wave machine. As a result of our experiments, we found that the sampling mode shows the best accuracy. We also found that the computational time of our method is faster than that of the exact solver when we tackle various QKPs defined on dense graphs.