# Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice

arXiv: https://arxiv.org/abs/2405.20384 · HTML: https://mlsanity.com/paper/2405.20384/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 79 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Minimal Gated Unit for Recurrent Neural Networks](https://mlsanity.com/paper/1603.09420/) (2016)
- [Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models](https://mlsanity.com/paper/2101.07243/) (2021)
- [Neural Error Mitigation of Near-Term Quantum Simulations](https://mlsanity.com/paper/2105.08086/) (2021)
- [Mutual Information Scaling and Expressive Power of Sequence Models](https://mlsanity.com/paper/1905.04271/) (2019)
- [Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz](https://mlsanity.com/paper/2011.08657/) (2020)
- [Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problems](https://mlsanity.com/paper/2207.08189/) (2022)
- [Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy](https://mlsanity.com/paper/2207.14314/) (2022)
- [Investigating Topological Order using Recurrent Neural Networks](https://mlsanity.com/paper/2303.11207/) (2023)

## Built on by (most cited first, 8 of 8)

- [Hyperbolic recurrent neural network as the first type of non-Euclidean neural quantum state ansatz](https://mlsanity.com/paper/2505.22083/) (2025)
- [Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo](https://mlsanity.com/paper/2605.13807/) (2026)
- [Adaptive Neural Quantum States: A Recurrent Neural Network Perspective](https://mlsanity.com/paper/2507.18700/) (2025)
- [Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States](https://mlsanity.com/paper/2604.08661/) (2026)
- [New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures](https://mlsanity.com/paper/2604.24337/) (2026)
- [Two-dimensional Hyperbolic RNN Neural Quantum State](https://mlsanity.com/paper/2606.25600/) (2026)
- [Large-scale portfolio optimization with variational neural annealing](https://mlsanity.com/paper/2507.07159/) (2025)
- [Hyperbolic Restricted Boltzmann Machine Neural Quantum State](https://mlsanity.com/paper/2609.26032/) (2026)

## Abstract (arXiv)

Rydberg atom array experiments have demonstrated the ability to act as powerful quantum simulators, preparing strongly-correlated phases of matter which are challenging to study for conventional computer simulations. A key direction has been the implementation of interactions on frustrated geometries, in an effort to prepare exotic many-body states such as spin liquids and glasses. In this paper, we apply two-dimensional recurrent neural network (RNN) wave functions to study the ground states of Rydberg atom arrays on the kagome lattice. We implement an annealing scheme to find the RNN variational parameters in regions of the phase diagram where exotic phases may occur, corresponding to rough optimization landscapes. For Rydberg atom array Hamiltonians studied previously on the kagome lattice, our RNN ground states show no evidence of exotic spin liquid or emergent glassy behavior. In the latter case, we argue that the presence of a non-zero Edwards-Anderson order parameter is an artifact of the long autocorrelations times experienced with quantum Monte Carlo (QMC) simulations, and we show that autocorrelations can be systematically reduced by increasing numerical effort. This result emphasizes the utility of autoregressive models, such as RNNs, in conjunction with QMC, to explore Rydberg atom array physics on frustrated lattices and beyond.