Resolution enhancement of one-dimensional molecular wavefunctions in plane-wave basis via quantum machine learning

TL;DR

This paper explores quantum machine learning to enhance the resolution of one-dimensional molecular wavefunctions in plane-wave basis, demonstrating improved fidelity over simple interpolation and discussing potential extensions to many-body systems.

Contribution

It introduces a quantum machine learning approach for super-resolution of molecular wavefunctions, showing improved accuracy and discussing generalization to complex electronic states.

Findings

ML models outperform linear interpolation in wavefunction fidelity

Including data-dependent information improves wavefunction quality

Accuracy decreases for unseen electronic configurations

Abstract

Super-resolution is a machine-learning technique in image processing which generates high-resolution images from low-resolution images. Inspired by this approach, we perform a numerical experiment of quantum machine learning, which takes low-resolution (low plane-wave energy cutoff) one-particle molecular wavefunctions in plane-wave basis as input and generates high-resolution (high plane-wave energy cutoff) wavefunctions in fictitious one-dimensional systems, and study the performance of different learning models. We show that the trained models can generate wavefunctions having higher fidelity values with respect to the ground-truth wavefunctions than a simple linear interpolation, and the results can be improved both qualitatively and quantitatively by including data-dependent information in the ansatz. On the other hand, the accuracy of the current approach deteriorates for wavefunctions calculated in electronic configurations not included in the training dataset. We also discuss the generalization of this approach to many-body electron wavefunctions.