The Category CNOT
Logic in Computer Science
2018-03-05 v2 Quantum Physics
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.
Cite
@article{arxiv.1707.02348,
title = {The Category CNOT},
author = {Robin Cockett and Cole Comfort and Priyaa Srinivasan},
journal= {arXiv preprint arXiv:1707.02348},
year = {2018}
}
Comments
In Proceedings QPL 2017, arXiv:1802.09737