We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming we develop a notion that is directly taken from concepts used in quantum computation. The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem. As an example we give the semantics of Selinger's language in terms of our weakest preconditions. We also cover some specific situations and exhibit an interesting link with stabilizers. † Ellie D'Hondt was funded by the FWO and the VUB (Flanders) and Prakash Panangaden was funded in part by a grant from NSERC (Canada) and in part by a visiting fellowship from EPSRC (U.K.).
Weakest preconditions appropriate for quantum computation are introduced in REF .