  We propose a notion of quantum control in a quantum programming language
which permits the superposition of finitely many quantum operations without
performing a measurement. This notion takes the form of a conditional construct
similar to the IF statement in classical programming languages. We show that
adding such a quantum IF statement to the QPL programming language simplifies
the presentation of several quantum algorithms. This motivates the possibility
of extending the denotational semantics of QPL to include this form of quantum
alternation. We give a denotational semantics for this extension of QPL based
on Kraus decompositions rather than on superoperators. Finally, we clarify the
relation between quantum alternation and recursion, and discuss the possibility
of lifting the semantics defined by Kraus operators to the superoperator
semantics defined by Selinger.
