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arXiv:2405.20384 · Communications Physics

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

Mohamed Hibat-Allah, Ejaaz Merali, Giacomo Torlai, Roger G. Melko, Juan Carrasquilla

Published Jul 25, 2025• 6 citations
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Abstract

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.

DOI
10.1038/s42005-025-02226-7

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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.
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Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. Due to long experimental preparation times, obtaining projective measurement data can be relatively slow for large arrays, which poses a challenge for state reconstruction methods such as tomography. Today, novel ground-state wave-function Ans\"atze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate how pretraining modern RNNs on even small amounts of data significantly reduces the convergence time for a subsequent variational optimization of the wave function. This suggests that essentially any amount of measurements obtained from a state prepared in an experimental quantum simulator could provide significant values for neural-network-based VMC strategies.
Programmable quantum simulators based on Rydberg atom arrays are a fast-emerging quantum platform, bringing together long coherence times, high-fidelity operations, and large numbers of interacting qubits deterministically arranged in flexible geometries. Today's Rydberg array devices are demonstrating their utility as quantum simulators for studying phases and phase transitions in quantum matter. In this paper, we show that unprocessed and imperfect experimental projective measurement data can be used to enhance in silico simulations of quantum matter, by improving the performance of variational Monte Carlo simulations. As an example, we focus on data spanning the disordered-to-checkerboard transition in a $16\ifmmode\times\else\texttimes\fi{}16$ square-lattice array [S. Ebadi et al., Nature (London) 595, 227 (2021)] and employ the data-enhanced variational Monte Carlo algorithm to train powerful autoregressive wave-function ans\"atze based on recurrent neural networks (RNNs). We observe universal improvements in the convergence times of our simulations with this hybrid training scheme. Notably, we also find that pretraining with experimental data enables relatively simple RNN ans\"atze to accurately capture phases of matter that are not learned with a purely variational training approach. Our work highlights the promise of hybrid quantum-classical approaches for large-scale simulation of quantum many-body systems, combining autoregressive language models with experimental data from existing quantum devices.
We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.
Rydberg atom arrays (RAA) have been advocated as a promising avenue for the quantum simulation of different exotic quantum states. Numerical predictions for the ground state properties of this experimental platform can, however, be challenging in two-dimensional setups. In particular, faithfully treating long-range interactions is often crucial for distinguishing the fate of competing phases, but it usually comes at considerable cost. Projected entangled-pair states (PEPS), optimized via a sampling-based approach, have been shown to deal with such terms on the same ground as shorter-range ones. In this work, we employ these tools to investigate debated physical questions in different frustrated geometries of RAA, from the emergence of spin-glass physics on the Kagomé lattice to topological order beyond the PXP model on the Ruby lattice. By that, we contribute to establishing PEPS as well-suited tools for creating digital twins of RAA experiments.
Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with state-of-the-art numerical techniques, making NQS a compelling alternative, in particular for the simulation of large, two-dimensional (2D) quantum systems. In this study, we show that recurrent neural network (RNN) wave functions can be employed to study systems relevant to current research in quantum many-body physics. Specifically, we employ a 2D tensorized gated RNN to explore the bosonic Hofstadter model with a variable local Hilbert space cutoff and long-range interactions. At first, we benchmark the RNN-NQS for the Hofstadter-Bose-Hubbard (HBH) Hamiltonian on a square lattice. We find that this method, despite the complexity of the wave function, is capable of efficiently identifying and representing most ground-state properties. Afterwards, we apply the method to an even more challenging model for current methods, namely, the Hofstadter model with long-range interactions. This model describes Rydberg-dressed atoms on a lattice subject to a synthetic magnetic field. We study systems of size up to $12\ifmmode\times\else\texttimes\fi{}12$ sites and identify three different regimes by tuning the interaction range and the filling fraction $\ensuremath{\nu}$. In addition to phases known from the HBH model at short-range interaction, we observe bubble crystals and Wigner crystals for long-range interactions. Especially interesting is the evidence of a bubble crystal phase on a lattice, as this gives experiments a starting point for the search of clustered liquid phases, possibly hosting non-Abelian anyon excitations. In our work, we show that NQS are an efficient and reliable simulation method for quantum systems, which are the subject of current research. In particular, we demonstrate the ability of this method to simulate challenging systems with long-range interactions.