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This study explores the Elephant Quantum Walk model with varied step-length distributions, revealing complex dynamical transitions and robust entanglement. The findings highlight the impact of interference and memory on quantum walker behavior.

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Area of Science:

  • Quantum mechanics
  • Complex systems
  • Statistical physics

Background:

  • The Elephant Quantum Walk model previously explored uniform step-length distributions, resulting in hyperballistic dynamics (variance ∝ t³).
  • Quantum walks are fundamental tools for quantum computation and simulation, exhibiting unique transport properties.

Purpose of the Study:

  • To extend the Elephant Quantum Walk model to a wider range of functional forms for time-dependent step-length distributions.
  • To investigate the impact of interference, memory, and long-range hopping on the walker's dynamical regimes.
  • To analyze the entanglement properties of the quantum walker.

Main Methods:

  • Theoretical modeling of quantum walks with generalized probability distributions for step-length.
  • Analysis of walker dynamics across different regimes (ballistic, diffusive, superdiffusive, hyperballistic).
  • Investigation of quantum entanglement in the coin space.

Main Results:

  • Multiple transitions between dynamical regimes (ballistic → diffusive → superdiffusive → ballistic → hyperballistic) were observed for non-hermitian coins.
  • The initial diffusive regime was suppressed when using Hadamard coins.
  • A robust asymptotic approach to maximal coin-space entanglement was confirmed.

Conclusions:

  • The functional form of the step-length distribution significantly influences quantum walk dynamics.
  • Interference, memory, and long-range hopping effects lead to rich, non-trivial dynamical behaviors.
  • The Elephant Quantum Walk model provides a versatile platform for studying complex quantum transport phenomena and entanglement.