Predicting Properties of Quantum Systems with Conditional Generative Models

TL;DR

This work proposes the use of conditional generative models to simultaneously represent a family of states, learning shared structures of different quantum states from measurements, and demonstrates that the method can accurately predict the quantum phases of square lattices of 13$\times$13 Rydberg atoms.

Abstract

Machine learning has emerged recently as a powerful tool for predicting properties of quantum many-body systems. For many ground states of gapped Hamiltonians, generative models can learn from measurements of a single quantum state to reconstruct the state accurately enough to predict local observables. Alternatively, classification and regression models can predict local observables by learning from measurements on different but related states. In this work, we combine the benefits of both approaches and propose the use of conditional generative models to simultaneously represent a family of states, learning shared structures of different quantum states from measurements. The trained model enables us to predict arbitrary local properties of ground states, even for states not included in the training data, without necessitating further training for new observables. We first numerically validate our approach on 2D random Heisenberg models using simulations of up to 45 qubits. Furthermore, we conduct quantum simulations on a neutral-atom quantum computer and demonstrate that our method can accurately predict the quantum phases of square lattices of 13$\times$13 Rydberg atoms.

Figures (14)

• Figure 1: Overview of our framework. The training pipeline of the conditional generative model is marked with solid black arrows, while the test pipeline is marked with dashed green arrows.
• Figure 2: Overview of the conditional generative model used for ground states of the 2D anti-ferromagnetic Heisenberg model.
• Figure 3: Predicting correlation functions of ground states of the 2D random anti-ferromagnetic Heisenberg model. a) Random Coupling graph from the test set. The graph determines the 2D random Heisenberg model (\ref{['eq:H-heisenberg']}), and is used to condition our generative model. The interaction strength is indicated by both thickness and color (thicker and darker means higher interaction strength). b) True and predicted two-point correlation functions (\ref{['eq:correlation-functions']}) for a ground state from the test set encoded by our generative model given the coupling graph. c) Root Mean Square Error (RMSE) between true and predicted correlation functions for systems of different sizes, for our conditional generative model (blue), Gaussian kernel (orange), and shadow tomography (green). Each point in the plot corresponds to the error of correlation predictions for different sites, averaged over Hamiltonians from the test set.
• Figure 4: a) Second-order Rényi subsystem entanglement entropies for subsystems of size at most two (\ref{['eq:renyi-entanglement-entropy']}). The conditional generative model is conditioned on the coupling graph in (b), which determines the Hamiltonian (\ref{['eq:H-heisenberg']}) of the 2D random Heisenberg model. The strength of the couplings is indicated by the width and color of the edges in the graph.
• Figure 5: RMSE between true and predicted entanglement entropy for subsystems of size at most two, for our conditional generative model (blue), Gaussian kernel (orange), and shadow tomography (green). For a given system size, each point in the plot corresponds to the error of the entropy prediction for a particular subsystem, averaged over Hamiltonians from the test set.