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

HAL 2026 Open access

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Authors: Alexandre Clément
DOI: 10.4230/lipics.lics.2026.28
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 Algebraic and Geometric Analysis Quantum Mechanics and Applications

Publication details

Journal / source
HAL
Volume
380
Pages
28:1–28:26
Publication date
20 July 2026
Language
EN