Algorithms and hardware for solving quadratic unconstrained binary optimization (QUBO) problems have made significant recent progress. This advancement has focused attention on formulating combinatorial optimization problems as quadratic polynomials. To improve the performance of solving large QUBO problems, it is essential to minimize the number of binary variables used in the objective function. In this paper, we propose a QUBO formulation that offers a bit capacity advantage over conventional quadratization techniques. As a key application, this formulation significantly reduces the number of binary variables required for score-based Bayesian network structure learning. Experimental results on $16$ instances, ranging from $37$ to $223$ variables, demonstrate that our approach requires fewer binary variables than quadratization by orders of magnitude. Moreover, an annealing machine that implement our formulation have outperformed existing algorithms in score maximization.

翻译：求解二次无约束二进制优化（QUBO）问题的算法与硬件近期取得了显著进展。这一进展促使人们将关注点转向如何将组合优化问题表述为二次多项式形式。为提升大规模QUBO问题的求解性能，最小化目标函数中使用的二进制变量数量至关重要。本文提出了一种QUBO公式构建方法，相较于传统二次化技术在比特容量方面具有优势。作为关键应用，该公式显著降低了基于评分的贝叶斯网络结构学习所需的二进制变量数量。在包含$37$至$223$个变量的$16$个实例上的实验结果表明，本方法所需的二进制变量数量比二次化方法减少了数个数量级。此外，基于该公式实现的退火机在评分最大化任务中超越了现有算法。