Quantum Feature Selection with Higher-Order Binary Optimization on Trapped-Ion Hardware

TL;DR

This paper introduces a quantum feature selection method using higher-order binary optimization on trapped-ion hardware, capturing complex feature dependencies and demonstrating promising results on classification datasets.

Contribution

It develops a novel HUBO-based quantum feature selection framework that models multivariate dependencies beyond quadratic terms, implemented on current trapped-ion quantum hardware.

Findings

Quantum approach yields competitive classification performance.

Hardware executions closely match noiseless simulations.

Selected feature subsets are compact and informative.

Abstract

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.