Denotational semantics for stabiliser quantum programs
Abstract
The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational semantics for stabiliser operations which include measurement, classically-controlled Pauli operators, and affine classical operations, in which quantum error-correcting codes are first-class objects. The operations are interpreted as certain affine relations over finite fields. This offers a conceptually motivated and computationally-tractable alternative to the standard operator-algebraic semantics of quantum programs (whose time complexity grows exponentially as the state space increases in size). We demonstrate the power of the resulting semantics by describing a small, proof-of-concept assembly language for stabiliser programs with fully-abstract denotational semantics.
Cite
@article{arxiv.2511.22734,
title = {Denotational semantics for stabiliser quantum programs},
author = {Robert I. Booth and Cole Comfort},
journal= {arXiv preprint arXiv:2511.22734},
year = {2025}
}