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Exact Thermalization Dynamics in the "Rule 54" Quantum Cellular Automaton.

Katja Klobas1, Bruno Bertini1, Lorenzo Piroli2,3

  • 1Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom.

Physical Review Letters
|May 7, 2021
PubMed
Summary

We analyzed the quantum Rule 54 automaton

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Quantum cellular automata (QCA) are discrete models of quantum computation.
  • Understanding thermalization in quantum systems is crucial for quantum information science.

Purpose of the Study:

  • To provide an analytic description of the out-of-equilibrium dynamics of the Rule 54 quantum cellular automaton.
  • To access the full thermalization dynamics at the microscopic level for low-entangled initial states.

Main Methods:

  • Analytic description of global evolution on finite subsystems using quantum channels.
  • Derivation of analytic formulas for local observables and Rényi entropies.

Main Results:

  • Rule 54 exhibits non-Markovian behavior and nonequilibrium features.
  • Demonstrated finite relaxation rates and interaction-induced dressing effects.
  • Provided exact solutions for thermalization dynamics at the microscopic level.

Conclusions:

  • Rule 54 serves as a rare example of an exactly solvable system for studying thermalization.
  • The findings offer insights into the nonequilibrium dynamics of interacting integrable many-body quantum systems.