Kavli Affiliate: Eliska Greplova
| First 5 Authors: D. O. Oriekhov, Guliuxin Jin, Eliska Greplova, ,
| Summary:
We study the dynamical localization of discrete time evolution of topological
split-step quantum random walk (QRW) on a single-site defect starting from a
uniform distribution. Using analytical and numerical calculations, we determine
the high localization probability regions in the parameter space of the quantum
walker. These regions contain two or more pairs of trapped states, forming near
a lattice defect. By investigating the spectral properties of the discrete-time
evolution operators, we show that these trapped states have large overlap with
the initial uniformly distributed state, thus offering a simple interpretation
of the localization effect. As this localization scheme could be interpreted as
a variation of spatial quantum search algorithm, we compare the localization
probability and time with other types of two-dimensional quantum walks that do
not have topological phases and realize localization time scaling similar to
Grover’s algorithm. Finally we show that mechanism of localization we
identified is robust against the influence of disorder.
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