Resource-Aware Hybrid Quantum Programming with General Recursion and Quantum Control

This paper introduces the hybrid quantum language with general recursion $\mathtt{Hyrql}$, driven towards resource-analysis. By design, $\mathtt{Hyrql}$ does not require the specification of an initial set of quantum gates and, hence, is well amenable towards a generic cost analysis. Indeed, languages using different sets of quantum gates lead to representations of quantum circuits whose complexity varies. Towards resource-analysis, a semantics-preserving compilation algorithm to simply-typed term rewrite systems is described; allowing a generic reuse of all known techniques for analyzing the complexity of term rewrite systems. We prove the versatility of this approach through many examples.