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Oxford Quantum Talks Archive

Coalgebraic walks, in quantum and Turing computation

Bart Jacobs, Radboud University Nijmegen
Flowin'Cat 2010, October 2010, University of Oxford

Non-deterministic, probabilistic and quantum walks will be described, from the perspective of coalgebras and monads. Non-deterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It will be shown that also quantum walks are coalgebras of a new monad, involving additional control structure. This new monad will also be used to describe Turing machines coalgebraically, namely as controlled `walks' on a tape.

[video] [streaming video] [slides]