Cole Comfort

Date: March 27, 2020

Time: 1:00 PM

Location: Zoom

Title: The ZX& calculus

Abstract: Consider ZX&, the fragment of the ZX calculus generated by the copying/addition Frobenius algebras, the not gate and the and gate.  I prove that this fragment is complete and universal for a prop of spans of sets, by freely adding units and counits to the inverse products of TOF (the category generated by the Toffoli gate and computational basis states/effects).  To prove completeness, I first show show that adding a counit to TOF is the same as computing the classical channels, which is the the same as the discrete Cartesian completion.  The completeness of ZX& is obtained via a two way translation between this extension of TOF with units and counits, and ZX&.