Unravelling quantum chaos using persistent homology

TL;DR

This paper introduces a topological data analysis method using persistent homology to characterize quantum chaos by analyzing quantum trajectories, enabling differentiation between regular and chaotic regimes in quantum systems.

Contribution

It presents a novel topological pipeline for quantum dynamics analysis, adapting classical attractor topology methods to quantum systems through persistent homology.

Findings

Successfully discriminates between regular and chaotic quantum regimes

Applies to limited measurement data in quantum experiments

Demonstrates effectiveness on a Kerr-nonlinear cavity system

Abstract

Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a topology-preserving embedding method that allows reconstructing dynamical attractors, the topologies of which can be used to identify chaotic behaviour. Open quantum systems can similarly exhibit non-trivial dynamics, but the existing toolkit for classification and quantification are still limited, particularly for experimental applications. In this work, we present a topological pipeline for characterizing quantum dynamics, which draws inspiration from the classical approach by using single quantum trajectory unravelings of the master equation to construct analogue 'quantum attractors' and extracting their topology using persistent homology. We apply the method to a periodically modulated Kerr-nonlinear cavity to discriminate parameter regimes of regular and chaotic phase using limited measurements of the system.