Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice
arXiv:2405.20384 · doi:10.1038/s42005-025-02226-7
Abstract
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.
15 pages, 7 figures, 6 tables. Link to GitHub repository: https://github.com/mhibatallah/RNNWavefunctions
References in corpus (54)
- Array Programming with NumPy
- Anyons in an exactly solved model and beyond
- The density-matrix renormalization group in the age of matrix product states
- Topological entanglement entropy
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- A Critical Review of Recurrent Neural Networks for Sequence Learning
- Detecting topological order in a ground state wave function
- Topological quantum memory
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Stochastic series expansion method with operator-loop update
- Spin-Glass Theory for Pedestrians
- Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- Ising models of quantum frustration
- Studying Two Dimensional Systems With the Density Matrix Renormalization Group
- Reconstructing quantum states with generative models
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
- Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
- Ground state entanglement and geometric entropy in the Kitaev's model
- Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
- Quantum phases of Rydberg atoms on a kagome lattice
- Two-dimensional periodic frustrated Ising models in a transverse field
- Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
- Quantum optimization with arbitrary connectivity using Rydberg atom arrays
- Numerical study of the chiral quantum phase transition in one spatial dimension
- Complex density wave orders and quantum phase transitions in a model of square-lattice Rydberg atom arrays
- Topological phases and quantum computation
- Empowering deep neural quantum states through efficient optimization
- Variational Benchmarks for Quantum Many-Body Problems
- High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
- Neural Error Mitigation of Near-Term Quantum Simulations
- A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
- Triangular lattice quantum dimer model with variable dimer density
- Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
- Theory of the Kagome Lattice Ising Antiferromagnet in Weak Transverse Field
- Emergent glassy behavior in a kagome Rydberg atom array
- Variational Monte Carlo with Large Patched Transformers
- Dynamics with autoregressive neural quantum states: application to critical quench dynamics
- Investigating Topological Order using Recurrent Neural Networks
- Aquila: QuEra's 256-qubit neutral-atom quantum computer
- Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays
- Iterative Retraining of Quantum Spin Models Using Recurrent Neural Networks
- Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
- Calculating Renyi Entropies with Neural Autoregressive Quantum States
- Trimer quantum spin liquid in a honeycomb array of Rydberg atoms
- Neural network approach to quasiparticle dispersions in doped antiferromagnets
- Enhancing variational Monte Carlo using a programmable quantum simulator
- Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problems
- Entanglement Entropy and Topological Order in Resonating Valence-Bond Quantum Spin Liquids
- Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy
- Transformer neural networks and quantum simulators: a hybrid approach for simulating strongly correlated systems