[Paper Review] Enhancing variational Monte Carlo using a programmable quantum simulator

M. Schuyler Moss, Sepehr Ebadi+5 more|arXiv (Cornell University)|Aug 4, 2023

Machine Learning in Materials ScienceMaterials Science3 citations

TL;DR

This paper introduces a hybrid quantum-classical framework that enhances variational Monte Carlo (VMC) simulations by pre-training recurrent neural network (RNN) wavefunction ansätze using raw, unprocessed projective measurement data from a Rydberg atom quantum simulator. The method achieves faster convergence and improved accuracy in capturing quantum phases—particularly the checkerboard order in a 16×16 Rydberg array—by leveraging experimental data to initialize the model before Hamiltonian-driven variational optimization, enabling even simple RNNs to learn complex many-body phases that pure VMC fails to capture.

ABSTRACT

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 $16 imes 16$ square lattice array [S. Ebadi et al. Nature 595, 227 (2021)] and employ data-enhanced variational Monte Carlo to train powerful autoregressive wavefunction ansätze 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 pre-training with experimental data enables relatively simple RNN ansätze 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.

Motivation & Objective

• To address the challenge of simulating large-scale quantum many-body systems where classical simulations are intractable and quantum devices produce limited, noisy data.
• To explore whether unprocessed experimental measurement data from programmable Rydberg atom arrays can improve the performance of variational Monte Carlo simulations.
• To develop a hybrid training scheme that combines data-driven pre-training with Hamiltonian-driven variational optimization to enhance wavefunction ansatz learning.
• To demonstrate that experimental data can provide critical initialization information that enables simpler models to capture complex quantum phases, such as the checkerboard order, which are difficult to learn via variational optimization alone.

Proposed method

• A recurrent neural network (RNN) wavefunction ansatz is initialized randomly and first trained on raw projective measurement data from a 16×16 Rydberg atom array, using fluorescent imaging data that captures only ground-state atoms.
• The RNN is pre-trained for a fixed number of steps on experimental data to learn representative configurations of the target quantum state, using a data-driven loss function.
• After pre-training, the model is fine-tuned using Hamiltonian-driven variational Monte Carlo, where the energy expectation value of the many-body Hamiltonian is minimized.
• The training alternates between data-driven and Hamiltonian-driven phases, with the data pre-training reducing the effective state space the model must explore during subsequent variational optimization.
• The RNN architecture uses gated recurrent units (GRUs) and is applied in both 1D and 2D configurations to assess the impact of connectivity on learning performance.
• Hyperparameters such as learning rates, number of hidden units, and training steps are tuned based on experimental parameters and model performance, with optimal data-driven steps selected via early stopping on energy minimization.

Experimental results

Research questions

• RQ1 Can unprocessed, imperfect experimental measurement data from a Rydberg atom array improve the convergence and accuracy of variational Monte Carlo simulations?
• RQ2 To what extent can data-driven pre-training of RNN wavefunction ansätze enable the model to learn complex quantum phases—such as the checkerboard order—that are difficult to capture via pure variational optimization?
• RQ3 Does the hybrid training scheme (data-first, then Hamiltonian-driven) reduce the number of training steps required to reach a low-energy state compared to purely variational training?
• RQ4 How does the architectural design of the RNN (1D vs. 2D) affect its ability to learn phase orderings when pre-trained on experimental data?
• RQ5 Can pre-training with experimental data provide a more effective initialization than random weights, especially in systems with complex sign structures or long-range order?

Key findings

• The hybrid data-enhanced variational Monte Carlo approach significantly accelerates convergence, with the 1D RNN achieving a converged energy value close to that of full quantum Monte Carlo simulations after only ~1400 training steps.
• Pre-training with experimental data enables the 1D RNN to accurately capture the checkerboard order parameter, which the same model fails to learn when trained purely via variational optimization.
• Even with limited data, the 2D RNN wavefunction benefits from pre-training, showing faster convergence and improved early-stage order parameter estimation compared to purely variational training.
• The order parameter values from the hybrid-trained 1D RNN closely match those obtained from full quantum Monte Carlo simulations, indicating high fidelity in ground state approximation.
• The data-enhancement strategy provides a more effective initialization than random weights, reducing the search space for the variational optimization and enabling models to reach physically meaningful configurations faster.
• The method demonstrates that experimental data, even without error mitigation or pre-processing, contains sufficient information to guide the learning of complex many-body wavefunctions in exotic quantum phases.