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.

arXiv:2609.19619 [quant-ph]

(or arXiv:2609.19619v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.19619 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

Supplemental_Material.pdf

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