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arXiv · 1707.02348

The Category CNOT

Robin Cockett·Cole Comfort·Priyaa Srinivasan
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Abstract

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.

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Robin Cockett, Cole Comfort, Priyaa Srinivasan. 2017-07-05. The Category CNOT. https://doi.org/10.4204/eptcs.266.18

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