Qutrit ZX-calculus is complete for stabilizer quantum mechanics
In this paper, we show that a qutrit version of ZX-calculus, with rules significantly different from that of the qubit version, is complete for pure qutrit stabilizer quantum mechanics, where state preparations and measurements are based on the three dimensional computational basis, and unitary oper...
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| Aineistotyyppi: | Conference item |
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Open Publishing Association
2018
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| _version_ | 1826292743574388736 |
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| author | Wang, Q |
| author_facet | Wang, Q |
| author_sort | Wang, Q |
| collection | OXFORD |
| description | In this paper, we show that a qutrit version of ZX-calculus, with rules significantly different from that of the qubit version, is complete for pure qutrit stabilizer quantum mechanics, where state preparations and measurements are based on the three dimensional computational basis, and unitary operations are required to be in the generalized Clifford group. This means that any equation of diagrams that holds true under the standard interpretation in Hilbert spaces can be derived diagrammatically. In contrast to the qubit case, the situation here is more complicated due to the richer structure of this qutrit ZX-calculus. |
| first_indexed | 2024-03-07T03:19:25Z |
| format | Conference item |
| id | oxford-uuid:b6ed4614-4d2d-4410-8520-c3b262911b62 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:19:25Z |
| publishDate | 2018 |
| publisher | Open Publishing Association |
| record_format | dspace |
| spelling | oxford-uuid:b6ed4614-4d2d-4410-8520-c3b262911b622022-03-27T04:44:36ZQutrit ZX-calculus is complete for stabilizer quantum mechanicsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:b6ed4614-4d2d-4410-8520-c3b262911b62Symplectic Elements at OxfordOpen Publishing Association2018Wang, QIn this paper, we show that a qutrit version of ZX-calculus, with rules significantly different from that of the qubit version, is complete for pure qutrit stabilizer quantum mechanics, where state preparations and measurements are based on the three dimensional computational basis, and unitary operations are required to be in the generalized Clifford group. This means that any equation of diagrams that holds true under the standard interpretation in Hilbert spaces can be derived diagrammatically. In contrast to the qubit case, the situation here is more complicated due to the richer structure of this qutrit ZX-calculus. |
| spellingShingle | Wang, Q Qutrit ZX-calculus is complete for stabilizer quantum mechanics |
| title | Qutrit ZX-calculus is complete for stabilizer quantum mechanics |
| title_full | Qutrit ZX-calculus is complete for stabilizer quantum mechanics |
| title_fullStr | Qutrit ZX-calculus is complete for stabilizer quantum mechanics |
| title_full_unstemmed | Qutrit ZX-calculus is complete for stabilizer quantum mechanics |
| title_short | Qutrit ZX-calculus is complete for stabilizer quantum mechanics |
| title_sort | qutrit zx calculus is complete for stabilizer quantum mechanics |
| work_keys_str_mv | AT wangq qutritzxcalculusiscompleteforstabilizerquantummechanics |