A proposal of quantum-inspired machine learning for medical purposes: An application case

Learning tasks are implemented via mappings of the sampled data set, including both the classical and the quantum framework. Biomedical data characterizing complex diseases such as cancer typically require an algorithmic support for clinical decisions, especially for early stage tumors that typify breast cancer patients, which are still controllable in a therapeutic and surgical way. Our case study consists of the prediction during the pre-operative stage of lymph node metastasis in breast cancer patients resulting in a negative diagnosis after clinical and radiological exams. The classifier adopted to establish a baseline is characterized by the result invariance for the order permutation of the input features, and it exploits stratifications in the training procedure. The quantum one mimics support vector machine mapping in a high-dimensional feature space, yielded by encoding into qubits, while being characterized by complexity. Feature selection is exploited to study the performances associated with a low number of features, thus implemented in a feasible time. Wide variations in sensitivity and specificity are observed in the selected optimal classifiers during cross-validations for both classification system types, with an easier detection of negative or positive cases depending on the choice between the two training schemes. Clinical practice is still far from being reached, even if the flexible structure of quantum-inspired classifier circuits guarantees further developments to rule interactions among features: this preliminary study is solely intended to provide an overview of the particular tree tensor network scheme in a simplified version adopting just product states, as well as to introduce typical machine learning procedures consisting of feature selection and classifier performance evaluation.