Bifurcation Curves of Two-Dimensional Quantum Walks

  title={Bifurcation Curves of Two-Dimensional Quantum Walks},
  author={Parker Kuklinski and Mark A. Kon},
The quantum walk differs fundamentally from the classical random walk in a number of ways, including its linear spreading and initial condition dependent asymmetries. Using stationary phase approximations, precise asymptotics have been derived for one-dimensional two-state quantum walks, one-dimensional three-state Grover walks, and two-dimensional four-state Grover walks. Other papers have investigated asymptotic behavior of a much larger set of two-dimensional quantum walks and it has been… 

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