Abstract
This chapter introduces quantum programs with classical control flows in the superposition-of-data paradigm. It first defines the syntax of a quantum extension of a while-language. The operational semantics of the quantum while-language is carefully presented, and the denotational semantics of quantum while-programs is systematically investigated. For convenience of the reader, the basics of lattice theory and domain theory needed in defining the denotational semantics are briefly reviewed. The quantum while-language is further extended by introducing recursion. Several semantics of recursive quantum programs with classical control are studied. As an illustrative example, Grover search is programmed in the language defined in this chapter.
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