Pivoting makes the ZX-calculus complete for real stabilizers
We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2014-12-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1307.7048v2 |
| _version_ | 1818322514952060928 |
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| author | Ross Duncan Simon Perdrix |
| author_facet | Ross Duncan Simon Perdrix |
| author_sort | Ross Duncan |
| collection | DOAJ |
| description | We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics. |
| first_indexed | 2024-12-13T10:58:01Z |
| format | Article |
| id | doaj.art-8282da89a1a742d4b0deb8d4e49f29b0 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-13T10:58:01Z |
| publishDate | 2014-12-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-8282da89a1a742d4b0deb8d4e49f29b02022-12-21T23:49:22ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802014-12-01171Proc. QPL 2013506210.4204/EPTCS.171.5:duncanperdrixPivoting makes the ZX-calculus complete for real stabilizersRoss Duncan0Simon Perdrix1 University of Strathclyde CNRS We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics.http://arxiv.org/pdf/1307.7048v2 |
| spellingShingle | Ross Duncan Simon Perdrix Pivoting makes the ZX-calculus complete for real stabilizers Electronic Proceedings in Theoretical Computer Science |
| title | Pivoting makes the ZX-calculus complete for real stabilizers |
| title_full | Pivoting makes the ZX-calculus complete for real stabilizers |
| title_fullStr | Pivoting makes the ZX-calculus complete for real stabilizers |
| title_full_unstemmed | Pivoting makes the ZX-calculus complete for real stabilizers |
| title_short | Pivoting makes the ZX-calculus complete for real stabilizers |
| title_sort | pivoting makes the zx calculus complete for real stabilizers |
| url | http://arxiv.org/pdf/1307.7048v2 |
| work_keys_str_mv | AT rossduncan pivotingmakesthezxcalculuscompleteforrealstabilizers AT simonperdrix pivotingmakesthezxcalculuscompleteforrealstabilizers |