A Complete Equational Theory for Real-Clifford+CH Quantum Circuits

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Alexandre Clément
Cited by: 0

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.

Fields of Study & Subjects

Quantum Computing Algorithms and Architecture Quantum Information and Cryptography Quantum Mechanics and Applications

Publication details

Journal / source
arXiv (Cornell University)
Publication date
6 February 2026
Language
EN
Document type
Preprint