Quon 3D language for quantum information.

Abstract:

:We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string-genus "joint relation," involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of the C∗-Hopf algebra relations, which are widely used in tensor networks. We obtain a 3D representation of the controlled NOT (CNOT) gate that is considerably simpler than earlier work, and a 3D topological protocol for teleportation.

authors

Liu Z,Wozniakowski A,Jaffe AM

doi

10.1073/pnas.1621345114

subject

Has Abstract

pub_date

2017-03-07 00:00:00

pages

2497-2502

issue

10

eissn

0027-8424

issn

1091-6490

pii

1621345114

journal_volume

114

pub_type

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