# Quantum Motional State Tomography with Non-Quadratic Potentials and Neural Networks

## TL;DR

This paper introduces a method combining non-quadratic potentials and neural networks to reconstruct unknown quantum motional states efficiently, with potential experimental applications.

## Contribution

It presents a novel approach using complex quantum dynamics and neural networks for motional state tomography in non-quadratic potentials.

## Key findings

- Neural networks can accurately reconstruct quantum states from position measurements.
- The method is feasible despite decoherence and potential uncertainties.
- Efficient state reconstruction is possible with measurements at different times.

## Abstract

We propose to use the complex quantum dynamics of a massive particle in a non-quadratic potential to reconstruct an initial unknown motional quantum state. We theoretically show that the reconstruction can be efficiently done by measuring the mean value and the variance of the position quantum operator at different instances of time in a quartic potential. We train a neural network to successfully solve this hard regression problem. We discuss the experimental feasibility of the method by analyzing the impact of decoherence and uncertainties in the potential.