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. |
ArXived at: https://dx.doi.org/10.4204/EPTCS.266.18 | bibtex | |
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