Diagnosing quantum transport from wave function snapshots

TL;DR

This paper introduces a data-driven method using principal component analysis on wave function snapshots to diagnose quantum transport in spin chains, revealing that data information spreading mirrors quantum transport dynamics.

Contribution

The study presents a novel, interpretable PCA-based approach to analyze quantum transport from wave function data, applicable to experimental and higher-dimensional systems without relying on Hamiltonian assumptions.

Findings

Data information spreading growth matches quantum transport exponents.

Method enables transport diagnostics with limited samples.

Applicable to experimental quantum simulator data and higher-dimensional systems.

Abstract

We study nonequilibrium quantum dynamics of spin chains by employing principal component analysis (PCA) on data sets of wave function snapshots and examine how information propagates within these data sets. The quantities we employ are derived from the spectrum of the sample second moment matrix, built directly from data sets. Our investigations on several interacting spin chains featuring distinct spin or energy transport reveal that the growth of data information spreading follows the same dynamical exponents as that of the underlying quantum transport of spin or energy. Specifically, our approach enables an easy, data-driven, and importantly interpretable diagnostic to track energy transport with a limited number of samples, which is usually challenging without any assumption on the Hamiltonian form. These observations are obtained at a modest finite size and evolution time, which aligns with experimental and numerical constraints. Our framework directly applies to experimental quantum simulator data sets of dynamics in higher-dimensional systems, where classical simulation methods usually face significant limitations and apply equally to both near- and far-from-equilibrium quenches.