We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to QUBO-based approaches, the proposed model includes one-, two-, and three-body interaction terms derived from mutual-information measures, enabling the objective function to capture feature relevance, pairwise redundancy, and higher-order statistical structure within a unified energy model. To suppress trivial all-selected solutions, we further include structured linear penalties that promote sparsity while preserving informative variables. The resulting HUBO instances are optimized with digitized counterdiabatic quantum optimization on IonQ Forte and compared against noiseless quantum simulation as well as two classical dimensionality-reduction baselines: SelectKBest based on mutual information and principal component analysis (PCA). We evaluate the proposed workflow on two benchmark classification datasets, namely the Gallstone dataset and the Spambase dataset, and analyze both predictive performance and selected-subset structure. The results show good qualitative agreement between hardware executions and noiseless simulations, supporting the feasibility of implementing higher-order feature-selection Hamiltonians on current trapped-ion processors. In addition, the quantum approach yields competitive classification performance while producing compact and informative feature subsets, highlighting the potential of higher-order quantum optimization for machine-learning preprocessing tasks.

翻译：我们提出了一种基于高阶无约束二元优化（HUBO）公式的量子特征选择框架，该框架明确纳入了超出标准二次编码的多元依赖关系。与基于QUBO的方法相比，该模型包含从互信息度量导出的单体、二体和三体相互作用项，使得目标函数能够在一个统一的能量模型中捕捉特征相关性、成对冗余和高阶统计结构。为了抑制琐碎的全选解，我们进一步引入结构化线性惩罚，在保持信息变量的同时促进稀疏性。生成的HUBO实例利用IonQ Forte上的数字化反绝热量子优化进行优化，并与无噪声量子模拟以及两种经典降维基线方法（基于互信息的SelectKBest和主成分分析（PCA））进行比较。我们在两个基准分类数据集（即胆结石数据集和垃圾邮件数据集）上评估了所提出的工作流程，并分析了预测性能和所选子集结构。结果表明，硬件执行与无噪声模拟之间具有良好的定性一致性，支持在现有捕获离子处理器上实现高阶特征选择哈密顿量的可行性。此外，量子方法在产生紧凑且信息丰富的特征子集的同时，达到了具有竞争力的分类性能，突显了高阶量子优化在机器学习预处理任务中的潜力。