[Alta-Logic] peripatetic seminar tomorrow

[Jonathan Gallagher]

*Location:* ICT 616, Friday November 24 at 11:15 am

See
http://peripatetic-seminar.cpsc.ucalgary.ca/wp/?event=cole-comfort-and-priyaa-srinivasan-or-priyaa-and-cole


Or below for details:

*Speaker: *Cole

*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
$\mathbb{Z}_2^n\to\mathbb{Z}_2^m$ with a circuit from $n\to m+k$ wires
consisting only of Toffoli gates (with $k$ 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 $\mathsf{PInj}$

*Speaker: *Priyaa

*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 CP*[FHilb]

Our goal is to move towards understanding the following:
Theorem:
Let C be a dagger compact closed category and C_{pure} be a subcategory of
C that inherits the dagger and compact closed structure. Suppose C_{pure}
has a decoherence structure with purification, then there exists an
invertible dagger functor from CP*[C_{pure}] -> C such that F(f \otimes g)
= F(f) \otimes F(g).
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