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Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation.

Di Luo1,2, Zhuo Chen1, Juan Carrasquilla3,4

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Researchers developed a new method for simulating open quantum systems using autoregressive neural networks. This approach offers a more accurate and computationally efficient way to understand complex quantum dynamics.

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Area of Science:

  • Quantum Science and Engineering
  • Quantum Information Theory
  • Computational Physics

Background:

  • Simulating open quantum systems is computationally intensive due to large Hilbert spaces.
  • Existing methods like Markov chain Monte Carlo have limitations in accuracy and efficiency.
  • Developing scalable methods for quantum dynamics is crucial for quantum technologies.

Purpose of the Study:

  • To present a novel approach for simulating open quantum system dynamics.
  • To leverage autoregressive neural networks for compact quantum state representation.
  • To improve the accuracy and efficiency of quantum dynamics simulations.

Main Methods:

  • Utilized an exact probabilistic formulation based on positive operator-valued measure.
  • Employed autoregressive neural networks for efficient quantum state representation and sampling.
  • Introduced 'string states' to enhance local correlation descriptions.
  • Developed algorithms for simulating Liouvillian superoperator dynamics and finding steady states.

Main Results:

  • The proposed method accurately tracks exact solutions for one- and two-dimensional systems.
  • Achieved higher accuracy compared to methods using restricted Boltzmann machines and Markov chain Monte Carlo.
  • Demonstrated efficient simulation of quantum dynamics and steady-state finding.
  • Showcased the potential for solving high-dimensional classical probabilistic differential equations.

Conclusions:

  • The developed approach offers a powerful and flexible tool for simulating open quantum systems.
  • This method provides a significant advancement in computational quantum physics.
  • The techniques are applicable to both quantum and classical high-dimensional problems.