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Machine learning approach to the Floquet-Lindbladian problem.

V Volokitin1, I Meyerov1, S Denisov2

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Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

We investigated if a quantum map can be generated by a time-independent Lindbladian. Machine learning methods and Choi matrix spectral properties reveal the answer is encoded in eigenvalues and eigenstates.

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Area of Science:

  • Quantum Information Theory
  • Quantum Dynamics
  • Machine Learning

Background:

  • Quantum Markovian evolution can be time-discrete (using completely positive trace-preserving maps) or time-continuous (using Lindbladians).
  • A key question is whether a given quantum map can be generated by a time-independent Lindbladian.

Purpose of the Study:

  • To explore machine learning methods for determining if a quantum map originates from a time-independent Lindbladian.
  • To validate the hypothesis that Choi matrix spectral properties encode this information.

Main Methods:

  • Applied various machine learning (ML) techniques to analyze quantum maps.
  • Investigated the spectral properties (eigenvalues and eigenstates) of the Choi matrix associated with quantum maps.
  • Utilized single-qubit models as a testbed for the ML and spectral analysis.

Main Results:

  • Machine learning methods show potential in answering the Lindbladian generation question.
  • The spectral properties of the Choi matrix, specifically eigenvalues and eigenstates, contain the information needed to determine Lindbladian generation.
  • Successfully validated the hypothesis using single-qubit models.

Conclusions:

  • The property of a quantum map being generatable by a time-independent Lindbladian is intrinsically linked to the spectral characteristics of its corresponding Choi matrix.
  • Machine learning offers a promising avenue for analyzing complex quantum dynamics and validating theoretical hypotheses.