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.
This work is a joint work with Takeshi Kimura and Kohtaro Kato. The detail is available from //arxiv.org/abs/2507.21569
报告人简介：Masahito Hayashi is a Presidential Chair Professor in the School of Data Science, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen), and a full Professor at the Graduate School of Mathematics, Nagoya University. He received his Ph.D. degrees in mathematics from Kyoto University in 1999. His research interests include classical and quantum information theory and classical and quantum statistical inference. He has published the book <Quantum Information Theory: Mathematical Foundation> from Graduate Texts in Physics (Springer) in 2016 and two other books <Group Representation for Quantum Theory> and <A Group Theoretic Approach to Quantum Information> (Springer). He is on the editorial board of New Journal of Physics and International Journal of Quantum Information. He received "the Information Theory Society Paper Award" for Information-Spectrum Approach to Second Order Coding Rate in Channel Coding in 2011. In 2016, he received the Japan Academy Medal from Japan Academy and the JSPS Prize from Japan Society for the Promotion of Science. In 2022, he was elected as an IMS Fellow and an IEEE Fellow.
