Categorifying the ZX-calculus
We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos. This can be used as a framework in which to study open networks and diagrammatic languages. We illustrate this framework with Coecke and Duncan's zx-calculus by constructing a bicategory w...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2018-02-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1704.07034v2 |
| _version_ | 1811305553673060352 |
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| author | Daniel Cicala |
| author_facet | Daniel Cicala |
| author_sort | Daniel Cicala |
| collection | DOAJ |
| description | We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos. This can be used as a framework in which to study open networks and diagrammatic languages. We illustrate this framework with Coecke and Duncan's zx-calculus by constructing a bicategory with the natural numbers for 0-cells, the zx-calculus diagrams for 1-cells, and rewrite rules for 2-cells. |
| first_indexed | 2024-04-13T08:27:24Z |
| format | Article |
| id | doaj.art-f5815e1de386446fa20f725c9bf29334 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-04-13T08:27:24Z |
| publishDate | 2018-02-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-f5815e1de386446fa20f725c9bf293342022-12-22T02:54:24ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802018-02-01266Proc. QPL 201729431410.4204/EPTCS.266.19:64Categorifying the ZX-calculusDaniel Cicala0 University of California, Riverside We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos. This can be used as a framework in which to study open networks and diagrammatic languages. We illustrate this framework with Coecke and Duncan's zx-calculus by constructing a bicategory with the natural numbers for 0-cells, the zx-calculus diagrams for 1-cells, and rewrite rules for 2-cells.http://arxiv.org/pdf/1704.07034v2 |
| spellingShingle | Daniel Cicala Categorifying the ZX-calculus Electronic Proceedings in Theoretical Computer Science |
| title | Categorifying the ZX-calculus |
| title_full | Categorifying the ZX-calculus |
| title_fullStr | Categorifying the ZX-calculus |
| title_full_unstemmed | Categorifying the ZX-calculus |
| title_short | Categorifying the ZX-calculus |
| title_sort | categorifying the zx calculus |
| url | http://arxiv.org/pdf/1704.07034v2 |
| work_keys_str_mv | AT danielcicala categorifyingthezxcalculus |