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Hyperbolic Restricted Boltzmann Machine Neural Quantum State

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

We construct the first type of non-Euclidean non-autoregressive neural quantum state (NQS) in the form of the hyperbolic Restricted Boltzmann Machine (HRBM), which is studied in the variational Monte-Carlo (VMC) setting of the Quantum Sherrington-Kirkpatrick (QSK) model whose ground state exhibits volume-law entanglement. Across a 512-fold increase in the Hilbert space dimension corresponding to a system size increase from $N=14$ to $N=24$, HRBM NQS robustly outperforms its Euclidean version, the RBM NQS, in terms of better ground state energy optimization as well as lower Renyi-2 $S_2$ and vo

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