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...
| Main Authors: | , |
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| Formato: | Artigo |
| Idioma: | English |
| Publicado em: |
Open Publishing Association
2012-10-01
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| Colecção: | Electronic Proceedings in Theoretical Computer Science |
| Acesso em linha: | http://arxiv.org/pdf/1110.2613v3 |
| _version_ | 1831834646059417600 |
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| author | Alex Lang Bob Coecke |
| author_facet | Alex Lang Bob Coecke |
| author_sort | Alex Lang |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-23T04:18:48Z |
| format | Article |
| id | doaj.art-34ad6bd8bc1e4d1893af1201bd388311 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-23T04:18:48Z |
| publishDate | 2012-10-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-34ad6bd8bc1e4d1893af1201bd3883112022-12-21T18:00:18ZengOpen 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 |
| spellingShingle | Alex Lang Bob Coecke Trichromatic Open Digraphs for Understanding Qubits Electronic Proceedings in Theoretical Computer Science |
| title | 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_short | Trichromatic Open Digraphs for Understanding Qubits |
| title_sort | trichromatic open digraphs for understanding qubits |
| url | http://arxiv.org/pdf/1110.2613v3 |
| work_keys_str_mv | AT alexlang trichromaticopendigraphsforunderstandingqubits AT bobcoecke trichromaticopendigraphsforunderstandingqubits |