Abstract
We study the dynamics of discrete-time quantum walk using quantum coin operations, and , in time-dependent periodic sequence. For the two-period quantum walk with the parameters and in the coin operations we show that the standard deviation is the same as the minimum of standard deviation obtained from one of the one-period quantum walks with coin operations or , . Our numerical result is analytically corroborated using the dispersion relation obtained from the continuum limit of the dynamics. Using the dispersion relation for one- and two-period quantum walks, we present the bounds on the dynamics of three- and higher-period quantum walks. We also show that the bounds for the two-period quantum walk will hold good for the split-step quantum walk which is also defined using two coin operators using and . Unlike the previous known connection of discrete-time quantum walks with the massless Dirac equation where coin parameter , here we show the recovery of the massless Dirac equation with nonzero parameters contributing to the intriguing interference in the dynamics in a totally nonrelativistic situation. We also present the effect of periodic sequence on the entanglement between coin and position space.
2 More- Received 22 November 2017
- Corrected 12 June 2018
DOI:https://doi.org/10.1103/PhysRevA.97.012116
©2018 American Physical Society
Physics Subject Headings (PhySH)
Corrections
12 June 2018
Correction: The surname of the second author contained an error and has been fixed.