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

2026-04-09

AI Summary

Standard autoregressive recurrent neural networks struggle to effectively model long-range quantum correlations exhibiting power-law decay. This work proposes a dilated recurrent neural network wave function, introducing dilated connections into neural quantum states for the first time. By explicitly embedding a geometric inductive bias for long-range interactions into its architecture, the model enhances representational capacity for such correlations while maintaining a forward computational complexity of $O(N \log N)$. Experimental results demonstrate that the proposed approach successfully reproduces the power-law two-point correlations characteristic of the critical one-dimensional transverse-field Ising model and accurately approximates the one-dimensional cluster state—a task challenging for conventional RNNs—thereby confirming its advantage in efficiently and precisely modeling strongly correlated quantum systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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 ans\"atze. 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.

Problem

• long-range correlations
• recurrent neural networks
• neural quantum states
• autoregressive models
• quantum many-body systems

Innovation

• dilated RNN
• neural quantum states
• long-range correlations
• autoregressive models
• power-law scaling