# Deep Neural Network Emulation of the Quantum-Classical Transition via Learned Wigner Function Dynamics

arXiv: https://arxiv.org/abs/2504.16334 · HTML: https://mlsanity.com/paper/2504.16334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 15 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 2 of 2)

- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [Neural Network Emulation of the Classical Limit in Quantum Systems via Learned Observable Mappings](https://mlsanity.com/paper/2504.10781/) (2025)

## Abstract (arXiv)

The emergence of classical behavior from quantum mechanics as Planck's constant hbar approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly learn the dynamical mapping from initial quantum state parameters (for Gaussian wave packets of the one-dimensional harmonic oscillator) and hbar to the parameters of the time-evolved Wigner function in phase space [4-6]. A comprehensive dataset of analytically derived time-evolved Wigner functions was generated, and a deep feedforward neural network with an enhanced architecture was successfully trained for this prediction task, achieving a final training loss of ~ 0.0390. The network demonstrates a significant and previously unrealized ability to accurately capture the underlying mapping of the Wigner function dynamics. This allows for a direct emulation of the quantum-classical transition by predicting the evolution of phase-space distributions as hbar is systematically varied. The implications of these findings for providing a new computational lens on the emergence of classicality are discussed, highlighting the potential of this direct phase-space learning approach for studying fundamental aspects of quantum mechanics. This work presents a significant advancement beyond previous efforts that focused on learning observable mappings [7], offering a direct route via the phase-space representation.