  Feature selection is critical in machine learning to reduce dimensionality
and improve model accuracy and efficiency. The exponential growth in feature
space dimensionality for modern datasets directly results in ambiguous samples
and redundant features, which can severely degrade classification accuracy.
Quantum machine learning offers potential advantages for addressing this
challenge. In this paper, we propose a novel method, quantum support vector
machine feature selection (QSVMF), integrating quantum support vector machines
with multi-objective genetic algorithm. QSVMF optimizes multiple simultaneous
objectives: maximizing classification accuracy, minimizing selected features
and quantum circuit costs, and reducing feature covariance. We apply QSVMF for
feature selection on a breast cancer dataset, comparing the performance of
QSVMF against classical approaches with the selected features. Experimental
results show that QSVMF achieves superior performance. Furthermore, The Pareto
front solutions of QSVMF enable analysis of accuracy versus feature set size
trade-offs, identifying extremely sparse yet accurate feature subsets. We
contextualize the biological relevance of the selected features in terms of
known breast cancer biomarkers. This work highlights the potential of
quantum-based feature selection to enhance machine learning efficiency and
performance on complex real-world data.
