A Restricted Boltzmann Machine with Quantum-State Visible Units
Abstract
We construct a restricted Boltzmann machine (RBM) whose visible input is a quantum state rather than a classical configuration. Each hidden unit carries a trainable quantum template prepared by a parametrized circuit and converts its overlap with the input into a feature. Treating quantum states as high-dimensional continuous visible objects creates nontrivial normalization and scaling problems. We regularize the continuous likelihood and derive two controlled high-dimensional limits, yielding a Hopfield-type network with continuous Hilbert-space patterns and a data-augmented Gram likelihood. The resulting algorithms are compact and use trainable circuit-prepared templates as measurement intermediaries between quantum data and classical optimization. Numerical simulations across several many-body systems demonstrate effective quantum-phase recognition and multicomponent feature extraction.
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BibTeX
@misc{zhang2026restricted,
title = {{A Restricted Boltzmann Machine with Quantum-State Visible Units}},
author = {Zhe-Hao Zhang and Yi-Cong Yu and Xiaoming Cai and Hai-Qing Lin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19619},
eprint = {2609.19619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19619},
}
RIS
TY - UNPB
TI - A Restricted Boltzmann Machine with Quantum-State Visible Units
AU - Zhe-Hao Zhang
AU - Yi-Cong Yu
AU - Xiaoming Cai
AU - Hai-Qing Lin
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19619
UR - https://arxiv.org/abs/2609.19619
AB - We construct a restricted Boltzmann machine (RBM) whose visible input is a quantum state rather than a classical configuration. Each hidden unit carries a trainable quantum template prepared by a parametrized circuit and converts its overlap with the input into a feature. Treating quantum states as high-dimensional continuous visible objects creates nontrivial normalization and scaling problems. We regularize the continuous likelihood and derive two controlled high-dimensional limits, yielding a Hopfield-type network with continuous Hilbert-space patterns and a data-augmented Gram likelihood. The resulting algorithms are compact and use trainable circuit-prepared templates as measurement intermediaries between quantum data and classical optimization. Numerical simulations across several many-body systems demonstrate effective quantum-phase recognition and multicomponent feature extraction.
ER -