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Quantum walks with sequential aperiodic jumps.

M A Pires1, S M Duarte Queirós1,2

  • 1Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro/RJ, Brazil.

Physical Review. E
|August 16, 2020
PubMed
Summary
This summary is machine-generated.

Aperiodic jumps in quantum walks (QW) slow down wave packet spreading, with the exponent depending on the jump sequence. These jumps also influence QW dynamics and enhance spin-lattice entanglement.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Information theory

Background:

  • Quantum walks (QW) are quantum analogues of classical random walks, exhibiting unique transport properties.
  • Aperiodicity in quantum systems can lead to novel phenomena and altered dynamics.
  • Understanding the interplay between aperiodicity and quantum walk evolution is crucial for developing quantum technologies.

Purpose of the Study:

  • To investigate the impact of aperiodic jump sequences on discrete-time quantum walks.
  • To analyze the effects of different coin operators (Hadamard and Fourier) on QW dynamics.
  • To explore how aperiodicity influences wave packet spreading, informational measures, and entanglement.

Main Methods:

  • Analysis of discrete-time quantum walks with Fibonacci, Thue-Morse, and Rudin-Shapiro jump sequences.
  • Utilizing generalized Hadamard and Fourier coin operators.
  • Calculation of wave packet spreading exponent (α), Shannon and von Neumann entropies, Inverse Participation Ratio, Jensen-Shannon dissimilarity, and kurtosis.

Main Results:

  • Aperiodic jumps lead to a slowdown in wave packet spreading (σ²(t)∼t^α), with the exponent α dependent on the aperiodicity type.
  • The exponent α shows sensitivity to the coin operator, with notable differences for Rudin-Shapiro and random protocols.
  • A nonmonotonic dependence of α on the coin operator's angle (θ) was observed, despite spatial and temporal homogeneity.
  • Informational measures and delocalization features reveal the impact of linear and nonlinear correlations in the jump sequences.

Conclusions:

  • Aperiodic jumps significantly modify quantum walk dynamics, inducing a slowdown in spreading and unique behaviors.
  • The choice of coin operator and the nature of aperiodicity critically influence the quantum walk's evolution.
  • Aperiodic protocols enhance spin-lattice entanglement, suggesting potential applications in quantum information processing.