A Complete Equational Theory for Real-Clifford+CH Quantum Circuits
Quantum Physics
2026-02-09 v1 Logic in Computer Science
Abstract
We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment, and prove that any other true equation can be derived from these. This is the first such completeness result for a finitely-generated, universal fragment of quantum circuits, with no parameterized gates and no need for ancillas.
Cite
@article{arxiv.2602.06644,
title = {A Complete Equational Theory for Real-Clifford+CH Quantum Circuits},
author = {Alexandre Clément},
journal= {arXiv preprint arXiv:2602.06644},
year = {2026}
}
Comments
Main body: 13 pages, appendix: 264 pages