Coalgebraic Walks, in Quantum and Turing Computation

The paper investigates non-deterministic, probabilistic and quantum walks, from the perspective of coalgebras and monads. Nondeterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It is shown that also quantum walks are coalgebras of a new monad, involving additional control structure. This new monad is also used to describe Turing machines coalgebraically, namely as controlled ‘walks’ on a tape.

• Type: Journal
• Year: 2011
• Where: FOSSACS
• Authors: Bart Jacobs
• Keywords: Control Structure, FOSSACS 2011, Monads, Powerset, Software Engineering