Abstract
The paper investigates non-deterministic, probabilistic and quantum walks, 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 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.
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Jacobs, B. (2011). Coalgebraic Walks, in Quantum and Turing Computation. In: Hofmann, M. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2011. Lecture Notes in Computer Science, vol 6604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19805-2_2
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DOI: https://doi.org/10.1007/978-3-642-19805-2_2
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