Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
Quantum Physics
2014-11-07 v1
Abstract
We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit equivalence rules. Within this framework, we show the first-order-only covariance of the Dirac QW. We then introduce the Clock QW and the Clock QCA, and prove that they are exactly discrete Lorentz covariant. The theory also allows for non-homogeneous Lorentz transforms, between non-inertial frames.
Cite
@article{arxiv.1404.4499,
title = {Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata},
author = {Pablo Arrighi and Stefano Facchini and Marcelo Forets},
journal= {arXiv preprint arXiv:1404.4499},
year = {2014}
}
Comments
21 pages, 15 figures