Bayesian network structure learning using quantum generative models

Bayesian network structure learning (BNSL) is a popular NP-hard optimization problem in the classical machine learning community. Given data, the network structure is optimized under the constraints of a directed acyclic graph and network scores using a cost function representing the constraints. In this study, we present BNSL using quantum generative models (QGMs) as a novel quantum machine learning application. QGMs are based on a quantum circuit composed of Pauli Y-rotation gates and controlled Pauli X or Z gates for quantum entanglement. Two real datasets are used to verify the comparative performance compared to classical counterpart GMs based on a three-layer neural network. For the training stage of the models, a hybrid quantum-classical framework is used. Due to the constraint-based cost function, classical data encoding is unnecessary, and the QGMs are trained so as to realize the desired output probability in one measurement. Simulation results show that QGMs achieve a comparative or better performance. In addition, we find a significant speed-up of the QGM compared to classical counterpart GMs. We believe that a combination of constraint-based cost functions and QGMs is useful to achieve such speed-ups.