Paper: A Complete Equational Theory for Real-Clifford+CH Quantum Circuits (at LICS 2026)

Authors: Alexandre Clément

Open access: https://doi.org/10.4230/LIPIcs.LICS.2026.28

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.

BibTeX

  @InProceedings{Clement-ACompleteEquational,
    author = 	 {Alexandre Clément},
    title = 	 {A Complete Equational Theory for Real-Clifford+CH Quantum Circuits},
    booktitle =  {Proceedings of the Forty-First Annual Symposium on Logic in Computer Science (LICS 2026)},
    year =	 {2026},
    month =	 {July}, 
    pages =      {28:1--28:26},
    location =   {Lisbon, Portugal}, 
    publisher =	 {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
    doi =        {10.4230/LIPIcs.LICS.2026.28}
  }