Trichromatic Open Digraphs for Understanding Qubits

Trichromatic Open Digraphs for Understanding Qubits

We introduce a trichromatic graphical calculus for quantum computing. The generators represent three complementary observables that are treated on equal footing, hence reflecting the symmetries of the Bloch sphere. We derive the Euler angle decomposition of the Hadamard gate within it as well as the...

Full description

Bibliographic Details
Main Authors: Alex Lang, Bob Coecke
Format: Article
Language:English
Published: Open Publishing Association 2012-10-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1110.2613v3
id doaj-34ad6bd8bc1e4d1893af1201bd388311
record_format Article
spelling doaj-34ad6bd8bc1e4d1893af1201bd3883112020-11-24T23:10:02ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802012-10-0195Proc. QPL 201119320910.4204/EPTCS.95.14Trichromatic Open Digraphs for Understanding QubitsAlex LangBob CoeckeWe introduce a trichromatic graphical calculus for quantum computing. The generators represent three complementary observables that are treated on equal footing, hence reflecting the symmetries of the Bloch sphere. We derive the Euler angle decomposition of the Hadamard gate within it as well as the so-called supplementary relationships, which are valid equations for qubits that were not derivable within Z/X-calculus of Coecke and Duncan. More specifically, we have: dichromatic Z/X-calculus + Euler angle decomposition of the Hadamard gate = trichromatic calculus. http://arxiv.org/pdf/1110.2613v3
collection DOAJ
language English
format Article
sources DOAJ
author Alex Lang
Bob Coecke
spellingShingle Alex Lang
Bob Coecke
Trichromatic Open Digraphs for Understanding Qubits
Electronic Proceedings in Theoretical Computer Science
author_facet Alex Lang
Bob Coecke
author_sort Alex Lang
title Trichromatic Open Digraphs for Understanding Qubits
title_short Trichromatic Open Digraphs for Understanding Qubits
title_full Trichromatic Open Digraphs for Understanding Qubits
title_fullStr Trichromatic Open Digraphs for Understanding Qubits
title_full_unstemmed Trichromatic Open Digraphs for Understanding Qubits
title_sort trichromatic open digraphs for understanding qubits
publisher Open Publishing Association
series Electronic Proceedings in Theoretical Computer Science
issn 2075-2180
publishDate 2012-10-01
description We introduce a trichromatic graphical calculus for quantum computing. The generators represent three complementary observables that are treated on equal footing, hence reflecting the symmetries of the Bloch sphere. We derive the Euler angle decomposition of the Hadamard gate within it as well as the so-called supplementary relationships, which are valid equations for qubits that were not derivable within Z/X-calculus of Coecke and Duncan. More specifically, we have: dichromatic Z/X-calculus + Euler angle decomposition of the Hadamard gate = trichromatic calculus.
url http://arxiv.org/pdf/1110.2613v3
work_keys_str_mv AT alexlang trichromaticopendigraphsforunderstandingqubits
AT bobcoecke trichromaticopendigraphsforunderstandingqubits
_version_ 1725608488215773184

Similar Items