Resource-Aware Quantum Programming with General Recursion and Quantum Control

TL;DR

This paper presents a resource-aware quantum programming language, Hyrql, that facilitates generic cost analysis and relates program runtime to quantum circuit size, enabling classical analysis techniques for quantum resource bounds.

Contribution

Introduction of Hyrql, a quantum language with general recursion and quantum control, designed for resource analysis without fixed gate sets, and linking runtime to quantum circuit complexity.

Findings

Hyrql supports resource analysis without specifying initial quantum gates.

It relates program runtime to the size of corresponding quantum circuits.

It captures functions computable in quantum polynomial time.

Abstract

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. Hence, it is well amenable towards a generic cost analysis, unlike languages that use different sets of quantum gates, which yield quantum circuits of distinct complexity. Regarding resource-analysis, we show how to relate the runtime of an expressive fragment of $\mathtt{Hyrql}$ programs with the size of the corresponding quantum circuits. We also manage to capture the class of functions computable in quantum polynomial time, which, by Yao's Theorem, corresponds to families of circuits of polynomial size. Consequently, this result paves the way for the use of termination and runtime-analysis techniques designed for classical programs to guarantee bounds on the size of quantum circuits.