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000643430 0247_ $$2arXiv$$aarXiv:2502.17562
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000643430 041__ $$aEnglish
000643430 088__ $$2arXiv$$aarXiv:2502.17562
000643430 082__ $$a530
000643430 1001_ $$aDemidik, Maria$$b0
000643430 245__ $$aExpressive equivalence of classical and quantum restricted Boltzmann machines
000643430 260__ $$c2025
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000643430 500__ $$a11 pages, 4 figures; supplementary material 6 pages, 1 figure
000643430 520__ $$aThe 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.
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000643430 536__ $$0G:(EU-Grant)101087126$$aQUEST - QUantum computing for Excellence in Science and Technology (101087126)$$c101087126$$fHORIZON-WIDERA-2022-TALENTS-01$$x1
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000643430 7001_ $$aTüysüz, Cenk$$b1
000643430 7001_ $$aPiatkowski, Nico$$b2
000643430 7001_ $$00000-0003-1718-1314$$aGrossi, Michele$$b3
000643430 7001_ $$0P:(DE-H253)PIP1003636$$aJansen, Karl$$b4$$eCorresponding author$$udesy
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000643430 9141_ $$y2025
000643430 915__ $$0StatID:(DE-HGF)0580$$2StatID$$aPublished
000643430 9201_ $$0I:(DE-H253)CQTA-20221102$$kCQTA$$lCentre f. Quantum Techno. a. Application$$x0
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