Mapping confinement potentials and charge densities of interacting quantum systems using conditional generative adversarial networks

TL;DR

This paper introduces a machine learning approach using conditional GANs to efficiently predict ground state densities and potentials in interacting quantum systems, reducing computational costs compared to traditional methods.

Contribution

It applies and optimizes a cGAN-based image translation model for quantum density and potential prediction, including inverse problem solutions, advancing computational quantum physics tools.

Findings

cGAN accurately predicts ground state densities from confinement potentials

The method reduces computational time compared to exact diagonalization

Inverse mapping from densities to potentials is feasible with the proposed approach

Abstract

Accurate and efficient tools for calculating the ground state properties of interacting quantum systems are essential in the design of nanoelectronic devices. The exact diagonalization method fully accounts for the Coulomb interaction beyond mean field approximations and it is regarded as the gold-standard for few electron systems. However, by increasing the number of instances to be solved, the computational costs become prohibitive and new approaches based on machine learning techniques can provide a significant reduction in computational time and resources, maintaining a reasonable accuracy. Here, we employ {\tt pix2pix}, a general-purpose image-to-image translation method based on conditional generative adversarial network (cGAN), for predicting ground state densities from randomly generated confinement potentials. Other mappings were also investigated, like potentials to non-interacting densities and the translation from non-interacting to interacting densities. The architecture of the cGAN was optimized with respect to the internal parameters of the generator and discriminator. Moreover, the inverse problem of finding the confinement potential given the interacting density can also be approached by the pix2pix mapping, which is an important step in finding near-optimal solutions for confinement potentials.