标题： 整数二进制编码HOBO公式中的不等式约束简化方法 显示英文标题

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

摘要： 本研究提出了一种简化高阶二元优化（HOBO）公式中不等式约束的新方法。 所提出的方法解决了与二次无约束二元优化（QUBO）公式相关的问题，特别是由于引入松弛变量而导致的计算复杂度增加和求解精度降低，以及由此产生的辅助量子比特数量的增长。 通过高效地整合约束条件，该方法提高了量子和经典求解器的计算效率和准确性。 通过将数值实验应用于组合优化问题，证明了所提出方法的有效性。 结果表明，该方法扩展了量子算法在高维问题中的适用性，并提高了经典优化求解器在涉及不等式约束的优化问题中的实用性。 显示英文摘要

摘要： 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.