Chapter 3

Syntax and semantics of quantum programs

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 ...

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