We propose the design of a programming language for quantum computing. Traditionally, quantum algorithms are frequently expressed at the hardware level, for instance in terms of the quantum circuit model or quantum Turing machines. These approaches do not encourage structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types. The language is functional in nature, statically typed, free of run-time errors, and has an interesting denotational semantics in terms of complete partial orders of superoperators.