A Probabilistic Graphical Model of Quantum Systems

Quantum systems are promising candidates of future computing and information processing devices. In a large system, information about the quantum states and processes may be incomplete and scattered. To integrate the distributed information we propose a quantum version of probabilistic graphical models. Variables in the model (quantum states and measurement outcomes) are linked by several types of operators (unitary, measurement, and merge/split operators). We propose algorithms for three machine learning tasks in quantum probabilistic graphical models: a belief propagation algorithm for inference of unknown states, an iterative algorithm for simultaneous estimation of parameter values and hidden states, and an active learning algorithm to select measurement operators based on observed evidence. We validate these algorithms on simulated data and point out future extensions toward a more comprehensive theory of quantum probabilistic graphical models.