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Discrete-time quantum walk dispersion control through long-range correlations.

A R C Buarque1,2, F S Passos2, W S Dias3

  • 1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Pernambuco, Brazil.

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Summary
This summary is machine-generated.

We explored quantum walks with long-range correlations. Tuning these correlations controls the spreading of quantum states, enabling dispersion control in quantum systems.

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Area of Science:

  • Quantum physics
  • Complex systems

Background:

  • Quantum walks are fundamental models in quantum computation and condensed matter physics.
  • Understanding the dynamics of quantum walks with disorder is crucial for developing robust quantum technologies.

Purpose of the Study:

  • To investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks.
  • To explore the impact of long-range spatial and temporal correlations on quantum walk spreading patterns.

Main Methods:

  • Utilized quantum coin operators with random inhomogeneity distribution.
  • Employed fractional Brownian motion with power-law spectrum (S(k)∼1/k^{ν}) to model correlations.
  • Conducted extensive numerical simulations averaging over many independent realizations.

Main Results:

  • Demonstrated that power-law correlated disorder leads to diverse spreading behaviors: localized, subdiffusive, diffusive, and superdiffusive (ballistic).
  • Showcased that the spreading patterns depend on the strength of correlation parameters.
  • Confirmed that dispersion control is achievable by manipulating correlation properties.

Conclusions:

  • Long-range correlations in quantum coin operators significantly influence quantum walk dynamics.
  • The study provides a method for controlling quantum state spreading in one-dimensional quantum walks.
  • Findings offer insights into designing quantum systems with tunable transport properties.