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

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

URL: http://arxiv.org/abs/2602.06644v1
Date: Fri, 06 Feb 2026 12:11:39 GMT
Title: A Complete Equational Theory for Real-Clifford+CH Quantum Circuits
Authors: Alexandre Clément,
Abstract summary: We give a simple set of equalities between circuits of this fragment, and prove that any other true equation can be derived from these.<n>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.
Score: 51.56484100374058
License: http://creativecommons.org/licenses/by/4.0/
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.

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