The Category CNOT

Robin Cockett
(University of Calgary)
Cole Comfort
(University of Calgary)
Priyaa Srinivasan
(University of Calgary)

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 ancillæ. 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.

In Bob Coecke and Aleks Kissinger: Proceedings 14th International Conference on Quantum Physics and Logic (QPL 2017), Nijmegen, The Netherlands, 3-7 July 2017, Electronic Proceedings in Theoretical Computer Science 266, pp. 258–293.
Published: 27th February 2018.

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