Quantum Walks...

Image source: Science Mag - 2D Walk Simulation

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 in diagrammatic representation in terms of a few local, circuit equivalence rules. Within this framework, we show that the first-order-only covariance of the Dirac QW. We then introduce the clock QW and the clock QCA, and prove that are exactly discrete Lorentz covariant. The theory also allows for non-homogeneous Lorentz transforms, between non-inertial frames.

Keywords: discrete Lorentz transformation, local Lorentz covariance, circuit transformation

New Journal of Physics:
Discrete Lorentz covariance for quantum walks and quantum cellular automata

Pablo Arrighi 1,2, Stefano Facchini 1 and Marcelo Forets 1
1. Univ Grenoble Alpes, LIG, F-38000 Grenoble, France
2. Université de Lyon, LIP, 46 allée dʼItalie, F-69008 Lyon, France