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He-Ran Wang1, Xiao-Yang Yang1,2, Zhong Wang1

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Researchers developed solvable quantum circuits for studying nonequilibrium dynamics. These circuits allow accurate calculation of local observables by exhibiting exact hidden Markovian subsystem dynamics, simplifying complex quantum system analysis.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Characterizing nonequilibrium dynamics in quantum many-body systems is a significant challenge.
  • Understanding how local subsystems evolve within larger quantum systems is crucial.
  • Existing methods often struggle with analytical tractability for long-time dynamics.

Purpose of the Study:

  • To systematically construct solvable nonintegrable quantum circuits.
  • To demonstrate exact hidden Markovian subsystem dynamics in these circuits.
  • To enable accurate calculation of local observables for arbitrary evolution times.

Main Methods:

  • Construction of solvable nonintegrable quantum circuits.
  • Application of the influence matrix method.
  • Analytical description of subsystem dynamics using sequential, time-local quantum channels with finite-dimensional ancillas.

Main Results:

  • Exact hidden Markovian subsystem dynamics were achieved in constructed quantum circuits.
  • The influence of the global system on a subsystem was analytically described.
  • A solvable condition for two-site gates was identified to realize the hidden Markovian property.

Conclusions:

  • The developed quantum circuits provide a powerful tool for studying quantum many-body dynamics.
  • The hidden Markovian property simplifies the analysis of local observables in complex quantum systems.
  • The approach is demonstrated with concrete examples, showcasing its versatility.