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Random logic networks: From classical Boolean to quantum dynamics.

Lucas Kluge1,2, Joshua E S Socolar3, Eckehard Schöll1,4

  • 1Potsdam Insitute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany.

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This study explores quantum Boolean networks, revealing how quantum effects alter perturbation propagation compared to classical systems. These quantum networks exhibit unique dynamics and information spread.

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Area of Science:

  • Quantum Information Science
  • Complex Systems Theory
  • Computational Neuroscience

Background:

  • Classical reversible Boolean networks model complex dynamics.
  • Quantum computing offers new paradigms for information processing.

Purpose of the Study:

  • Investigate the dynamical properties of quantum generalizations of classical Boolean networks.
  • Analyze perturbation propagation in these quantum networks.

Main Methods:

  • Encoding node states as qubits.
  • Supplementing Boolean logic with controlled bit-flip and Hadamard operations.
  • Employing synchronous updating schemes for qubit evolution.

Main Results:

  • Observed periodic or quasiperiodic behavior in quantum networks.
  • Analyzed single-site perturbation propagation in networks with input degree one.
  • Identified nonclassical mechanisms for perturbation spread.

Conclusions:

  • Quantum networks exhibit distinct dynamical properties compared to classical counterparts.
  • Nonclassical perturbation propagation significantly alters state evolution and Hamming distance dynamics.