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Topics
Quantum Circuit Design Gate Engineering
Quantum Simulation
Entanglement Theory Quantum Correlations
The Category CNOT
arXiv
Authors: Robin Cockett, Cole Comfort, Priyaa Srinivasan
Year
2017
Paper ID
44813
Status
Preprint
Abstract Read
~2 min
Abstract Words
68
Citations
N/A
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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- 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.
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