  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.
