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Simulation Complexity of Open Quantum Dynamics: Connection with Tensor Networks.

I A Luchnikov1,2, S V Vintskevich2,3, H Ouerdane1

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Summary
This summary is machine-generated.

Simulating open quantum systems is challenging due to large reservoir sizes. This study introduces a timeline reservoir network (TRN) to create effective, smaller reservoirs for accurate open quantum dynamics modeling.

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Area of Science:

  • Quantum Physics
  • Computational Physics

Background:

  • Simulating open quantum systems is computationally intensive due to the large Hilbert space of many-body reservoirs.
  • Existing methods struggle to efficiently model the complex dynamics arising from system-environment interactions.

Purpose of the Study:

  • To develop an efficient method for modeling the dynamics of open quantum systems.
  • To introduce a novel tensor network approach for representing reservoir dynamics.

Main Methods:

  • Application of a tensor network approach in the time domain.
  • Development of the timeline reservoir network (TRN) with a one-dimensional tensor network structure.
  • Approximation of the TRN using matrix product concepts, analogous to spin-chain states.

Main Results:

  • Demonstrated that effective small reservoirs can be defined for modeling open quantum dynamics.
  • Derived sufficient bond dimensions for the approximated TRN based on key physical parameters.
  • Showcased the bond dimension as a complexity measure for open quantum dynamics.

Conclusions:

  • The TRN provides an efficient and accurate method for simulating open quantum dynamics.
  • This approach simplifies complex system-environment interactions by reducing reservoir size.
  • Opens avenues for novel numerical and machine learning-based methods in quantum dynamics.