The category CNOT: Robin Cockett

ICE-TCS seminar #325

  • 8.1.2019, 12:15 - 13:00

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ICE-TCS seminar #325

Date and time: Tuesday, 8 January 2019, 12:10-13:00
Location: Room M1.20 (note the new room for the spring 2019 semester)
Speaker:  Robin Cockett (University of Calgary, Canada) WWW: http://pages.cpsc.ucalgary.ca/~robin/
Title: The category CNOT

Abstract: The talk describes the process of sorting out the identities that the quantum and reversible gate CNOT satisfies.  Somewhat surprisingly, although it has become of increasing importance as quantum computers come on line, the problem of what identities the CNOT gate (and ancillae) satisfy remained open until this work.

To solve the problem involved understanding "discrete inverse categories" which were explored in Brett Giles's PhD thesis (under my direction) and having a bright, hard working, and highly motivated undergraduate student -- Cole Comfort.   Cole solved most of the problem in his undergraduate final year project under my direction.  In the end he had some help from Priyaa Srinivasan (a PhD student of mine).

The techniques used in the proof are quite straightforward but involve some discrete inverse category tricks which were, perhaps, not available to other researchers.  The work gives a nice illustration of the importance of abstract mathematics in solving practical problems.