Quantum Bayes AI

Quantum Bayesian AI (Q-B) is an emerging field that levers the computational gains available in Quantum computing. The promise is an exponential speed-up in many Bayesian algorithms. Our goal is to apply these methods directly to statistical and machine learning problems. We provide a duality between classical and quantum probability for calculating of posterior quantities of interest. Our framework unifies MCMC, Deep Learning and Quantum Learning calculations from the viewpoint from von Neumann's principle of quantum measurement. Quantum embeddings and neural gates are also an important part of data encoding and feature selection. There is a natural duality with well-known kernel methods in statistical learning. We illustrate the behaviour of quantum algorithms on two simple classification algorithms. Finally, we conclude with directions for future research.