Structuring quantum effects: superoperators as arrows

J. K. Vizzotto, T. Altenkirch, A. Sabry

Published:

We show that the model of quantum computation based on density matrices and
superoperators can be decomposed in a pure classical (functional) part and an
effectful part modeling probabilities and measurement. The effectful part can
be modeled using a generalization of monads called arrows. We express the
resulting executable model of quantum computing in the programming language
Haskell using its special syntax for arrow computations. The embedding in
Haskell is however not perfect: a faithful model of quantum computing requires
type capabilities which are not directly expressible in Haskell.