Topological-Like Features in Diagrammatical Quantum Circuits
Abstract
In this paper, we revisit topological-like features in the extended Temperley--Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We perform these quantum circuits and derive characteristic equations for them with the help of topological-like operations. Furthermore, we comment on known diagrammatical approaches to quantum information phenomena from the perspectives of both tensor categories and topological quantum field theories. Moreover, we remark on the proposal for categorical quantum physics and information to be described by dagger ribbon categories.
Cite
@article{arxiv.quant-ph/0703196,
title = {Topological-Like Features in Diagrammatical Quantum Circuits},
author = {Yong Zhang and Louis H. Kauffman},
journal= {arXiv preprint arXiv:quant-ph/0703196},
year = {2008}
}
Comments
v1: Latex. v2,v3: original proposals in v1 are stated in a physical style. This manuscript is a formal written version of Y. Zhang's talk at the workshop "Cats, Kets and Cloisters", Computing Laboratory, Oxford University, July 17-23, 2006