Classification of Autism Spectrum Disorder involving Metabolites and Quantum Feature Selection

Introduction: 
Autism Spectrum Disorder (ASD) is a neurodevelopmental condition with a prevalence of one in 31 in 2022 [1] among 8 years old children in the United States. Biomarker based approaches provide a promising avenue for earlier and potentially more precise diagnosis [2]. However, metabolomic measurements can generate hundreds or even thousands of features per patient, while the number of available patients in a clinical trial is limited. This imbalance between feature dimensionality and sample size creates a high-dimensional classification problem in which models can easily overfit the data. As a result, identifying a small and stable subset of features is essential for building reliable classification models.

Feature selection methods aim to address this challenge by preserving discriminative information while reducing model complexity and improving generalization [3]. However, classical methods such as exhaustive search require evaluation of all possible feature combinations, making them computationally and runtime expensive or even infeasible as feature dimensionality increases.

Quantum optimization methods [4-5] provide a potential framework for addressing combinatorial feature selection problems more efficiently. In this study, we formulate ASD metabolomic feature selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem [6]. The QUBO problem is solved using bias-field digitized counterdiabatic quantum optimization (BF-DCQO) [7] on IBM gate-based quantum hardware. The objective of this work is to evaluate whether quantum optimization can identify near optimal feature subsets for ASD classification while demonstrating runtime advantages over classical methods.

Materials and Methods: 
Four ASD metabolomic datasets [8-10] were used in this study. Due to the limitations of current quantum hardware, including qubit count, noise, and decoherence, subsets of up to 60 metabolomic features were evaluated. The feature selection problem was formulated as a QUBO problem in which binary variables represented whether a feature was selected. The proposed objective function combined a Fisher score feature importance term with a covariance pair-wise feature redundancy penalization term to identify feature subsets with high discriminative scores while minimizing redundant information between selected features. A tunable weighting parameter controlled the balance between feature importance and redundancy penalization.

The resulting QUBO Hamiltonian was solved using BF-DCQO on IBM gate-based superconducting quantum hardware. The method first initializes the quantum system in the ground state of a simple Hamiltonian and then adiabatically evolves the system toward the problem Hamiltonian representing the QUBO objective. During this evolution, the quantum state is guided toward lower energy configurations corresponding to candidate feature subsets. BF-DCQO introduces counterdiabatic driving terms and bias fields to suppress non-adiabatic transitions and improve convergence toward the final low energy state on noisy intermediate scale quantum (NISQ) devices.

The finally selected feature subsets, i.e., the set of metabolites used for classification of autism, were evaluated using classical machine learning classifiers and Leave-One-Out Cross-Validation. Performance and runtime were compared against classical exhaustive search and mutual-information-based QUBO feature selection approaches.

Results, Conclusions, and Discussions: 
The proposed QUBO objective function consistently identified metabolomic feature subsets that achieved strong ASD classification performance across datasets and classifiers. Across most experiments, the proposed QUBO objective produced subsets with classification performance close to classical exhaustive feature search while demonstrating improved accuracy compared to commonly used mutual information-based QUBO objectives.

Classical exhaustive search rapidly became computationally infeasible as the number of candidates features increased. For example, exhaustive evaluation of the best subset of 5 features from a set of 24 metabolites required approximately 19.88 seconds, while exhaustive evaluation of choosing a subset of 5 metabolites from 60 measurements required approximately 1781.23 seconds. In comparison, the BF-DCQO based QUBO pipeline maintained relatively stable runtimes of approximately 30–32 seconds across both feature spaces. However, current limitations including restricted qubit count, circuit depth, gate noise, and decoherence still constrain the size of problems that can be directly explored on NISQ devices.