The Category CNOT
| Autor: | Priyaa Varshinee Srinivasan, Robin Cockett, Cole Comfort |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Logic in Computer Science Pure mathematics FOS: Physical sciences Inverse 01 natural sciences lcsh:QA75.5-76.95 Set (abstract data type) 03 medical and health sciences Computer Science::Emerging Technologies 0302 clinical medicine Controlled NOT gate Mathematics::Category Theory 0103 physical sciences 010306 general physics Commutative property Mathematics Quantum Physics lcsh:Mathematics Symmetric monoidal category lcsh:QA1-939 16. Peace & justice Logic in Computer Science (cs.LO) 030221 ophthalmology & optometry lcsh:Electronic computers. Computer science Affine transformation Quantum Physics (quant-ph) Vector space |
| Zdroj: | QPL Electronic Proceedings in Theoretical Computer Science, Vol 266, Iss Proc. QPL 2017, Pp 258-293 (2018) |
| ISSN: | 2075-2180 |
| DOI: | 10.4204/eptcs.266.18 |
| Popis: | We exhibit a complete set of identities for CNOT, the symmetric monoidal category generated by the controlled-not gate, the swap gate, and the computational ancillae. We prove that CNOT is a discrete inverse category. Moreover, we prove that CNOT is equivalent to the category of partial isomorphisms of finitely-generated non-empty commutative torsors of characteristic 2. Equivalently this is the category of affine partial isomorphisms between finite-dimensional Z2 vector spaces. Comment: In Proceedings QPL 2017, arXiv:1802.09737 |
| Databáze: | OpenAIRE |
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