# A Logic for Recursive Quantum Programs

arXiv: https://arxiv.org/abs/1812.00349 · HTML: https://mlsanity.com/paper/1812.00349/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Taxonomy of migration scenarios for Qiskit refactoring using LLMs](https://mlsanity.com/paper/2506.07135/) (2025)

## Abstract (arXiv)

Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursion will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of non-recursive quantum programs. However, there are as yet no general methods for reasoning about recursive procedures in quantum computing. We fill the gap in this paper by presenting a logic for recursive quantum programs. This logic is an extension of quantum Hoare logic for quantum While-programs. The (relative) completeness of the logic is proved, and its effectiveness is shown by a running example: fixed-point Grover's search.