CoqQ: Foundational Verification of Quantum Programs

TL;DR

CoqQ is a foundational framework embedded in Coq for verifying quantum programs, combining a quantum programming language, a formal logic, and practical proof techniques, demonstrated through numerous examples.

Contribution

It introduces a deeply embedded quantum programming language and a formally verified program logic within Coq, enabling rigorous reasoning about quantum algorithms.

Findings

Formal soundness of the program logic established

Concise specifications using Dirac expressions demonstrated

Verification process optimized with local and parallel reasoning

Abstract

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive program logic for proving properties of programs. CoqQ is foundational: the program logic is formally proved sound with respect to a denotational semantics based on state-of-art mathematical libraries (mathcomp and mathcomp analysis). CoqQ is also practical: assertions can use Dirac expressions, which eases concise specifications, and proofs can exploit local and parallel reasoning, which minimizes verification effort. We illustrate the applicability of CoqQ with many examples from the literature.