U(1) symmetric recurrent neural networks for quantum state reconstruction

TL;DR

This paper demonstrates that enforcing U(1) symmetry in recurrent neural networks enhances the efficiency and stability of quantum state reconstruction, particularly for the ground state of the XY model, aiding rapid feedback in quantum simulations.

Contribution

The study introduces a U(1) symmetry-enforced RNN approach for quantum state reconstruction, improving training stability and efficiency in modeling the XY model ground state.

Findings

U(1) symmetry enforcement improves early training efficiency.

Symmetry-enforced RNNs stabilize training by reducing gradient issues.

Enhanced performance benefits rapid quantum simulation feedback loops.

Abstract

Generative models are a promising technology for the enhancement of quantum simulators. These machine learning methods are capable of reconstructing a quantum state from experimental measurements, and can aid in the calculation of physical observables. In this paper, we employ a recurrent neural network (RNN) to reconstruct the ground state of the spin-1/2 XY model, a prototypical Hamiltonian explored in trapped ion simulators. We explore its performance after enforcing a U(1) symmetry, which was recently shown by Hibat-Allah et al. [Phys. Rev. Research 2, 023358 (2020)] to preserve the autoregressive nature of the RNN. By studying the reconstruction of the XY model ground state from projective measurement data, we show that imposing U(1) symmetry on the RNN significantly increases the efficiency of learning, particularly in the early epoch regime. We argue that this performance increase may result from the tendency of the enforced symmetry to alleviate vanishing and exploding gradients, which helps stabilize the training process. Thus, symmetry-enforced RNNs may be particularly useful for applications of quantum simulators where a rapid feedback between optimization and circuit preparation is necessary, such as in hybrid classical-quantum algorithms.