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Unravelling quantum chaos using persistent homology
Harvey Cao1, Daniel Leykam1, Dimitris G Angelakis1,2,3
1Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore.
Physical Review. E
|May 18, 2023
Summary
We present a topological pipeline to analyze quantum dynamics, identifying chaotic behavior in quantum systems using persistent homology. This method helps classify complex quantum phases with limited experimental data.
Area of Science:
- Quantum physics
- Complex systems analysis
- Topological data analysis
Background:
- Topological data analysis (TDA) offers powerful methods for extracting insights from complex datasets.
- Classical systems analysis uses TDA to identify chaotic dynamics by reconstructing attractors.
- Characterizing complex dynamics in open quantum systems remains a challenge due to limited analytical and experimental tools.
Purpose of the Study:
- To develop a topological pipeline for characterizing quantum dynamics.
- To adapt classical TDA methods for analyzing open quantum systems.
- To enable the classification of quantum dynamical regimes using limited measurements.
Main Methods:
- Utilizing single quantum trajectory unravelings of the master equation to construct analog quantum attractors.
- Applying persistent homology to extract topological features from these quantum attractors.
- Implementing the pipeline on a periodically modulated Kerr-nonlinear cavity.
Main Results:
- Successfully constructed analog quantum attractors from quantum trajectories.
- Extracted topological signatures to differentiate between regular and chaotic quantum phases.
- Demonstrated the method's efficacy in classifying parameter regimes with limited data.
Conclusions:
- The developed topological pipeline provides a novel approach for characterizing quantum dynamics.
- This framework allows for the identification of chaotic behavior in open quantum systems.
- The method shows promise for experimental applications requiring classification of quantum phases.
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