  The main contribution of the present paper is the introduction of a simple
yet expressive hybrid-dynamic logic for describing quantum programs. This
version of quantum logic can express quantum measurements and unitary
evolutions of states in a natural way based on concepts advanced in (hybrid and
dynamic) modal logics. We then study Horn clauses in the hybrid-dynamic quantum
logic proposed, and develop a series of results that lead to an initial
semantics theorem for sets of clauses that are satisfiable. This shows that a
significant fragment of hybrid-dynamic quantum logic has good computational
properties, and can serve as a basis for defining executable languages for
specifying quantum programs. We set the foundations of logic programming in
this fragment by proving a variant of Herbrand's theorem, which reduces the
semantic entailment of a logic-programming query by a program to the search of
a suitable substitution.
