# Certified Quantum Computation in Isabelle/HOL

arXiv: https://arxiv.org/abs/2012.13925 · HTML: https://mlsanity.com/paper/2012.13925/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2020.

## Built on by (most cited first, 2 of 2)

- [Lean-QIT: Towards a Formal Infrastructure for Quantum Information Theory](https://mlsanity.com/paper/2607.09632/) (2026)
- [AxQM: A Textbook-Scale Benchmark for Formal Proof Synthesis in a Library of Finite-Dimensional Quantum Mechanics](https://mlsanity.com/paper/2609.05157/) (2026)

## Abstract (arXiv)

In this article we present an ongoing effort to formalise quantum algorithms and results in quantum information theory using the proof assistant Isabelle/HOL. Formal methods being critical for the safety and security of algorithms and protocols, we foresee their widespread use for quantum computing in the future. We have developed a large library for quantum computing in Isabelle based on a matrix representation for quantum circuits, successfully formalising the no-cloning theorem, quantum teleportation, Deutsch's algorithm, the Deutsch-Jozsa algorithm and the quantum Prisoner's Dilemma. We discuss the design choices made and report on an outcome of our work in the field of quantum game theory.