Variational quantum algorithms to estimate rank, quantum entropies, fidelity, and Fisher information via purity minimization

Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, entropies, Bures fidelity and Fisher information mixed states are developed. In addition, variations these VQAs also adapted to perform other useful functions state learning approximate fractional inverses. The common theme shared by proposed is their cost all based on minimizing purity a state. Strategies mitigate or avoid problem exponentially vanishing function gradients discussed.