Bifurcation Curves of TwoDimensional Quantum Walks
Abstract
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 onedimensional twostate quantum walks, onedimensional threestate Grover walks, and twodimensional fourstate Grover walks. Other papers have investigated asymptotic behavior of a much larger set of twodimensional quantum walks and it has been shown that in special cases the regions of polynomial decay can be parameterized. In this paper, we show that these regions of polynomial decay are bounded by algebraic curves which can be explicitly computed. We give examples of these bifurcation curves for a number of twodimensional quantum walks.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1905.00057
 Bibcode:
 2019arXiv190500057K
 Keywords:

 Quantum Physics;
 Computer Science  Discrete Mathematics
 EPrint:
 In Proceedings QSQW 2020, arXiv:2004.01061