Journal Article

PUBDB-2025-01234

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Expressive equivalence of classical and quantum restricted Boltzmann machines

Demidik, M. (Corresponding author)DESY* ; Tüysüz, C. ; Piatkowski, N. ; Grossi, M. ; Jansen, K. (Corresponding author)DESY*

2025
Springer Nature London

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Please use a persistent id in citations: doi:10.1038/s42005-025-02353-1  doi:10.3204/PUBDB-2025-01234

Report No.: arXiv:2502.17562

Abstract: The development of generative models for quantum machine learning has faced challenges such as trainability and scalability. A notable example is the quantum restricted Boltzmann machine (QRBM), where non-commuting Hamiltonians make gradient evaluation computationally demanding, even on fault-tolerant devices. In this work, we propose a semi-quantum restricted Boltzmann machine (sqRBM), a model designed to overcome difficulties associated with QRBMs. The sqRBM Hamiltonian commutes in the visible subspace while remaining non-commuting in the hidden subspace, enabling us to derive closed-form expressions for output probabilities and gradients. Our analysis shows that, for learning a given distribution, a classical model requires three times more hidden units than an sqRBM. Numerical simulations with up to 100 units validate this prediction. With reduced resource demands, sqRBMs provide a feasible framework for early quantum generative models.

Note: 11 pages, 4 figures; supplementary material 6 pages, 1 figure

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Contributing Institute(s):

1. Centre f. Quantum Techno. a. Application (CQTA)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. QUEST - QUantum computing for Excellence in Science and Technology (101087126) (101087126)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2025

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Demidik, M. ; Tüysüz, C. ; Piatkowski, N. ; Grossi, M. ; Jansen, K. (Corresponding author)DESY*
Expressive equivalence of classical and quantum restricted Boltzmann machines
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