Unravelling quantum chaos using persistent homology

Topological data analysis is a powerful framework for extracting useful topological information from complex data sets. 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 behavior. Open quantum systems can similarly exhibit nontrivial dynamics, but the existing toolkit for classification and quantification are still limited, particularly for experimental applications. In this paper, 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 analog quantum attractors and extract their topology using persistent homology. We apply the method to a periodically modulated Kerr-nonlinear cavity to discriminate parameter regimes of regular and chaotic phases using limited measurements of the system.