Principal component analysis of wavefunction snapshots in non-equilibrium dynamics

TL;DR

This paper applies principal component analysis to wavefunction snapshots in non-equilibrium quantum dynamics, revealing connections to observables and extending to higher-order correlations.

Contribution

It introduces a transformation that maximizes information in principal components, linking data features to physical observables in quantum dynamics.

Findings

Maximized information content in the largest principal component.

Connected principal components to specific quantum observables.

Extended the method to extract higher-order correlations.

Abstract

We study non-equilibrium quantum dynamics by performing principal component analysis on the data sets of wavefunction snapshots. We show that a specific transformation of the data sets maximizes the information content in the largest principal component and further enables its connection to certain observables. This connection enables us to explain the dynamical features revealed by such a dimensionality-reduction scheme. We demonstrate this using quantum dynamics of the Heisenberg spin chain, starting from different initial states, and further extend the approach to extract higher-order correlations. Our framework should also be applicable to other unsupervised machine-learning methods based on dimensionality-reduction schemes and is highly relevant to experiments with quantum simulators, including those in higher dimensions.