Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs
Quantum Physics
2015-05-13 v1
Abstract
I obtain the dynamics of the continuous time quantum walk on a -dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main result of arXiv:quant-ph/0606050 which proved this limit for the infinite line. By highlighting the main features of the limiting procedure, I then extend it to general graphs. For a given discrete time quantum walk on a general graph, I single out the type of continuous dynamics (Hamiltonians) that can be obtained as a limit of the discrete time dynamics.
Cite
@article{arxiv.0902.3496,
title = {Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs},
author = {Domenico D'Alessandro},
journal= {arXiv preprint arXiv:0902.3496},
year = {2015}
}