A Simplification Method for Inequality Constraints in Integer Binary Encoding HOBO Formulations

TL;DR

This paper introduces a new simplification technique for inequality constraints in HOBO formulations, improving computational efficiency and accuracy for quantum and classical solvers in high-dimensional combinatorial optimization.

Contribution

It presents a novel method that simplifies inequality constraints in HOBO, reducing auxiliary qubits and enhancing solver performance.

Findings

Improved solution accuracy in quantum and classical solvers.

Reduced auxiliary qubits in HOBO formulations.

Enhanced applicability of quantum algorithms to high-dimensional problems.

Abstract

This study proposes a novel method for simplifying inequality constraints in Higher-Order Binary Optimization (HOBO) formulations. The proposed method addresses challenges associated with Quadratic Unconstrained Binary Optimization (QUBO) formulations, specifically the increased computational complexity and reduced solution accuracy caused by the introduction of slack variables and the resulting growth in auxiliary qubits. By efficiently integrating constraints, the method enhances the computational efficiency and accuracy of both quantum and classical solvers. The effectiveness of the proposed approach is demonstrated through numerical experiments applied to combinatorial optimization problems. The results indicate that this method expands the applicability of quantum algorithms to high-dimensional problems and improves the practicality of classical optimization solvers for optimization problems involving inequality constraints.