Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States

Quantum Physics [Submitted on 9 Apr 2026] Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States Asif Bin Ayub, Amine Mohamed Aboussalah, Mohamed Hibat-Allah Neural Quantum States based on autoregressive recurrent neural network (RNN) wave functions enable efficient sampling without Markov-chain autocorrelation, but standard RNN architectures are biased toward finite-length correlations and can fail on states with long-range dependencies. A common response is to adopt transformer-style self-attention, but this typically comes with substantially higher computational and memory overhead. Here we introduce dilated RNN wave functions, where recurrent units access distant sites through dilated connections, injecting an explicit long-range inductive bias while retaining a favorable \mathcal{O}(N \log N) forward pass scaling. We show analytically that dilation changes the correlation geometry and can induce power-law correlation scaling in a simplified linearized and perturbative setting. Numerically, for the critical 1D transverse-field Ising model, dilated RNNs reproduce the expected power-law connected two-point correlations in contrast to the exponential decay typical of conventional RNN ansätze. We further show that the dilated RNN accurately approximates the one-dimensional Cluster state, a paradigmatic example with long-range conditional correlations that has previously been reported to be challenging for RNN-based wave functions. These results highlight dilation as a simple geometric mechanism for building correlation-aware autoregressive neural quantum states. Comments: 16 pages, 4 figures, and 1 table Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG); Computational Physics (physics.comp-ph) Cite as: arXiv:2604.08661 [quant-ph]   (or arXiv:2604.08661v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.08661 Focus to learn more Submission history From: Mohamed Hibat-Allah [view email] [v1] Thu, 9 Apr 2026 18:00:04 UTC (683 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.dis-nn cs cs.LG physics physics.comp-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)