Unravelling quantum chaos using persistent homology
- URL: http://arxiv.org/abs/2211.15100v2
- Date: Wed, 14 Dec 2022 06:44:17 GMT
- Title: Unravelling quantum chaos using persistent homology
- Authors: Harvey Cao, Daniel Leykam, Dimitris G. Angelakis
- Abstract summary: 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.
We present a topological pipeline for characterizing quantum dynamics, which draws inspiration from the classical approach.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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