A Quantum-Inspired Approach to Supervised Multi-Class Classification

Classical feature vectors are encoded as density operators, each class is represented by a quantum centroid, and binary classification is performed using the Helstrom minimum-error state-discrimination strategy.

The framework is extended to multi-class classification using the Pretty Good Measurement (PGM), avoiding conventional one-versus-one and one-versus-rest approaches by discriminating multiple classes within a single quantum-state-discrimination protocol. We also introduce the k-copy (kkk-PGM) classifier and its implementation via quantum circuits, and show how PGM-based classifiers can be combined with quantum-inspired oversampling methods such as QSMOTE to address highly imbalanced datasets.

Two main application areas are presented. In biomedical imaging, the framework supports automated analysis of clonogenic assays using spatial, colour and texture features, and has been applied to radiomic data for lung-cancer subtyping and prostate-cancer risk stratification. In quantum physics, it classifies quantum states by distinguishing entangled, separable and product states, and is evaluated on ensembles of randomly generated mixed states.

This framework establishes quantum-state discrimination as a unified paradigm for supervised learning, applicable to both classical and quantum data while addressing practical challenges such as multi-class classification and class imbalance.