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

2026-04-29

AI Summary

This work addresses the limitations of traditional feature selection methods in modeling high-order variable dependencies and the restricted expressivity of existing quantum approaches, which are largely confined to quadratic optimization. The authors propose a quantum feature selection framework based on Higher-Order Unconstrained Binary Optimization (HUBO), introducing for the first time a high-order Hamiltonian that incorporates three-body interactions. Feature interactions up to third order are quantified using mutual information, and structured sparsity regularization is integrated to enhance interpretability. Implemented on the IonQ Forte trapped-ion quantum processor using a digital reverse annealing algorithm, the method yields compact yet highly discriminative feature subsets on the Gallstone and Spambase datasets, achieving classification performance that matches or surpasses classical baselines such as SelectKBest and PCA, thereby demonstrating the feasibility and advantage of high-order quantum feature selection.

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.

Problem

• Quantum Feature Selection
• Higher-Order Binary Optimization
• Multivariate Dependencies
• Sparsity
• Trapped-Ion Quantum Hardware

Innovation

• Higher-Order Binary Optimization
• Quantum Feature Selection
• Trapped-Ion Quantum Computing
• Mutual Information
• Counterdiabatic Quantum Optimization