Quantum recursion
Abstract
This chapter continues the studies of quantum programs with quantum control flows. We first define the syntax of quantum recursive programs and present a series examples, namely recursive quantum walks. It is shown that second quantization – a mathematical framework for dealing with quantum systems where the number of particles may vary – is required to define the semantics of quantum recursive programs. For convenience of the reader, we introduce the basics of second quantization needed in this chapter. Then the operational and denotational (fixed-point) semantics of quantum recursive programs in the free Fock space (of quantum coins) are defined, and their equivalence is established. Finally, the semantics ...
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