# Cole Comfort and Priyaa Srinivasan (or Priyaa and Cole)

Date: November 24, 2017

Time: 11:15

Location: ICT616

Talk

Title: A Complete Classification of the Toffoli Gate with Ancillary bits
Abstract:
The Toffoli gate is a universal gate for classical reversible computation.  This means that if we are allowed to fix the values of certain inputs and outputs (called ancillary bits), we can simulate any Boolean function from with a circuit from wires consisting only of Toffoli gates (with extra ignored outputs).

Iwama found a complete set of identities for circuits solely consisting of Toffoli gates.  I present a complete set of identities for the symmetric monoidal category generated by the Toffoli gate \emph{and ancillary bits}.  I also provide a normal form for these circuits and prove an equivalence of categories into a subcategory of
Title: Structures for decoherence

Abstract:
This talk will introduce and develop the structure required for studying
decoherence in certain monoidal categories.  Our driving example is a
decoherence structure in
Our goal is to move towards understanding the following:
Theorem:
Let C be a dagger compact closed category and be a subcategory of C that inherits the dagger and compact closed structure. Suppose has a decoherence structure with purification, then there exists an invertible dagger functor  such that .