2 research outputs found
Qubit state transfer via discrete-time quantum walks
We propose a scheme for perfect transfer of an unknown qubit state via the
discrete-time quantum walk on a line or a circle. For this purpose, we
introduce an additional coin operator which is applied at the end of the walk.
This operator does not depend on the state to be transferred. We show that
perfect state transfer over an arbitrary distance can be achieved only if the
walk is driven by an identity or a flip coin operator. Other biased coin
operators and Hadamard coin allow perfect state transfer over finite distances
only. Furthermore, we show that quantum walks ending with a perfect state
transfer are periodic.Comment: 13 pages, 5 figure
Two-dimensional quantum walk under artificial magnetic field
We introduce the Peierls substitution to a two-dimensional discrete-time
quantum walk on a square lattice to examine the spreading dynamics and the
coin-position entanglement in the presence of an artificial gauge field. We use
the ratio of the magnetic flux through the unit cell to the flux quantum as a
control parameter. For a given flux ratio, we obtain faster spreading for a
small number of steps and the walker tends to be highly localized around the
origin. Moreover, the spreading of the walk can be suppressed and decreased
within a limited time interval for specific rational values of flux ratio. When
the flux ratio is an irrational number, even for a large number of steps, the
spreading exhibit diffusive behavior rather than the well-known ballistic one
as in the classical random walk and there is a significant probability of
finding the walker at the origin. We also analyze the coin-position
entanglement and show that the asymptotic behavior vanishes when the flux ratio
is different from zero and the coin-position entanglement become nearly maximal
in a periodic manner in a long time range.Comment: 7 pages, 5 figures, sections 3 and 4 revise