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Non-Markovian dynamical maps: numerical processing of open quantum trajectories.

Javier Cerrillo1, Jianshu Cao1

  • 1Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.

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This study introduces a novel method using non-Markovian transfer tensors to predict open quantum system dynamics. This approach efficiently compresses initial state information for long-term trajectory prediction and analysis.

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Area of Science:

  • Quantum physics
  • Quantum information science
  • Statistical mechanics

Background:

  • Open quantum systems evolve complex dynamics influenced by their environment.
  • Initial system evolution contains crucial information about long-term behavior.
  • Predicting quantum trajectories requires efficient methods to handle environmental correlations.

Purpose of the Study:

  • To develop a general approach for extracting and compressing information from initial quantum system trajectories.
  • To enable accurate and efficient long-term state propagation of open quantum systems.
  • To reconstruct dynamical operators from observed quantum trajectories.

Main Methods:

  • Utilizing non-Markovian dynamical maps to define transfer tensors.
  • Compressing initial trajectory information into non-Markovian transfer tensors.
  • Assuming time-translational invariance for state propagation.
  • Equivalence to solving the Nakajima-Zwanzig equation.

Main Results:

  • Demonstration of the coherent-to-incoherent transition based on quantum dissipation strength.
  • Prediction of noncanonical equilibrium distributions arising from system-bath entanglement.
  • Successful reconstruction of system Hamiltonian and memory kernel from quantum trajectories.
  • Accurate and efficient propagation of quantum states over extended time scales.

Conclusions:

  • The non-Markovian transfer tensor method (TTM) provides a powerful tool for analyzing and predicting open quantum system dynamics.
  • TTM facilitates the understanding of quantum dissipation and system-environment interactions.
  • The framework is generalizable to other physical observables for trajectory learning and manipulation.