# Integrating Neural Networks with a Quantum Simulator for State Reconstruction

## TL;DR

This paper presents a method combining neural networks with a quantum simulator to reconstruct quantum states from experimental data, effectively handling measurement errors and capturing complex observables.

## Contribution

It introduces a neural network approach, specifically using RBMs, integrated with quantum hardware for accurate state reconstruction considering experimental errors.

## Key findings

- Successfully reconstructed quantum states from Rydberg simulator data.
- Captured complex observables like Rénnyi mutual information.
- Mitigated measurement errors with a novel regularization technique.

## Abstract

We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator, by means of a neural network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine (RBM) wavefunctions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis, and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the R\'enyi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.