Structured quantum learning via em algorithm for Boltzmann machines

Abstract

Quantum Boltzmann machines (QBMs) are generative models with potential advantages in quantum machine learning, yet their training is fundamentally limited by the barren plateau problem, where gradients vanish exponentially with system size. We introduce a quantum version of the em algorithm, an information-geometric generalization of the classical Expectation-Maximization method, which circumvents gradient-based optimization on non-convex functions. Implemented on a semi-quantum restricted Boltzmann machine (sqRBM) -- a hybrid architecture with quantum effects confined to the hidden layer -- our method achieves stable learning and outperforms gradient descent on multiple benchmark datasets. These results establish a structured and scalable alternative to gradient-based training in QML, offering a pathway to mitigate barren plateaus and enhance quantum generative modeling.