SICSA DVF Professor Robin Cockett “The category CNOT: finding a complete set of identities for the CNOT gate”

Date(s) - 07/11/2018
2:15 am - 3:00 pm

Heriot Watt University

SICSA DVF Professor Robin Cockett, Department of Computing Science at the University of Calgary will be giving a public lecture at Heriot Watt University

Talk: “The category CNOT: finding a complete set of identities for the CNOT gate”

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.

Bio: Prof. J. R. B. Cockett (1952) is a category theorist and computer scientist working in proof theory, computability and complexity, programming languages and semantics, categorical quantum information theory, and abstract differential geometry. After his PhD in Mathematics at the University of Leeds in 1979, he has worked in Essex (for Marconi research), Tennessee (US), Sydney (Australia), and since 1991 has been at the University of Calgary (Canada), where is a professor of computer science. He has developed three programming languages, Chartity, LQPL, and MPL, and is known for introducing and studying restriction categories, Turing categories, differential categories, and tangent categories.

Professor Cockett is being hosted by Dr Chris Heunen, University of Edinburgh

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