Quantum-inspired classification based on quantum state discrimination

We present quantum-inspired algorithms for classification tasks inspired by the problem of quantum state discrimination. By construction, these algorithms can perform multiclass classification, prevent overfitting, and generate probability outputs. While they could be implemented on a quantum computer, we focus here on classical implementations of such algorithms. The training of these classifiers involves Semi-Definite Programming. We also present a relaxation of these classifiers that utilizes Linear Programming (but that can no longer be interpreted as a quantum measurement). Additionally, we consider a classifier based on the Pretty Good Measurement (PGM) and show how to implement it using an analogue of the so-called Kernel Trick, which allows us to study its performance on any number of copies of the input state. We evaluate these classifiers on the MNIST and MNIST-1D datasets and find that the PGM generally outperforms the other quantum-inspired classifiers and performs comparably to standard classifiers.