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. 2025 Jul 7;12(8):nwaf269. doi: 10.1093/nsr/nwaf269

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© The Author(s) 2025. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Figure 2. — An RBM architecture with a parameter vector (corresponding to an amplitude RBM with and a phase RBM with ). Each RBM features a set of visible neurons (orange circles) and a set of hidden neurons (green circles) and consists of weights connecting the layers, and the biases and coupled to visible and hidden neurons, respectively. A Gibbs distribution (with normalization omitted) is obtained via and the distribution over the visible (hidden) layer is obtained by marginalization over the hidden (visible) degrees of freedom [11]. Given visible binary outcomes, the marginal distribution of hidden units is calculated as . Based on the sampled hidden configuration, the marginal distribution of visible units is calculated as . Two RBMs are trained to minimize the difference between the actual wave function and the reconstructed wave function (see Equation (15) for detailed information).

Inline graphic — An RBM architecture with a parameter vector (corresponding to an amplitude RBM with and a phase RBM with ). Each RBM features a set of visible neurons (orange circles) and a set of hidden neurons (green circles) and consists of weights connecting the layers, and the biases and coupled to visible and hidden neurons, respectively. A Gibbs distribution (with normalization omitted) is obtained via and the distribution over the visible (hidden) layer is obtained by marginalization over the hidden (visible) degrees of freedom [11]. Given visible binary outcomes, the marginal distribution of hidden units is calculated as . Based on the sampled hidden configuration, the marginal distribution of visible units is calculated as . Two RBMs are trained to minimize the difference between the actual wave function and the reconstructed wave function (see Equation (15) for detailed information).