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Discrete-time quantum walk with feed-forward quantum coin.

Yutaka Shikano1, Tatsuaki Wada2, Junsei Horikawa3

  • 11] Research Center of Integrative Molecular Systems (CIMoS), Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan [2] Institute for Quantum Studies, Chapman University, Orange, California 92866, USA.

Scientific Reports
|March 22, 2014
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Summary
This summary is machine-generated.

We introduce a novel feed-forward quantum walk model that exhibits anomalous slow diffusion, differing from the ballistic transport of standard quantum walks. This discrete model offers new insights into quantum dynamics.

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Area of Science:

  • Quantum mechanics
  • Complex systems
  • Dynamical systems

Background:

  • Discrete models like cellular automata are key to understanding dynamical systems.
  • The connection between discrete models and continuous analogues is complex.
  • Discrete-time quantum walks are quantum analogues of cellular automata, exhibiting quantum dynamical behavior.

Purpose of the Study:

  • To generalize discrete-time quantum walks on a line.
  • To introduce a feed-forward quantum coin model dependent on the previous coin state.
  • To analyze the transport properties of this new model.

Main Methods:

  • Generalization of the discrete-time quantum walk on a line.
  • Introduction of a feed-forward quantum coin mechanism.
  • Analysis of diffusion characteristics and comparison with conventional models.

Main Results:

  • The proposed feed-forward quantum walk model demonstrates anomalous slow diffusion.
  • This slow diffusion is characterized by the porous-medium equation.
  • Conventional discrete-time quantum walks exhibit ballistic transport.

Conclusions:

  • The feed-forward quantum coin model represents a significant departure from standard quantum walks.
  • This model provides a new framework for studying anomalous diffusion in quantum systems.
  • The findings highlight the rich and varied dynamics possible in discrete quantum models.