Minimal Equational Theories for Quantum Circuits
Year: 2024
Type: conference-paper
Abstract: We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one which states that a multi-control 2π rotation is nothing but the identity. Our work improves on the recent complete equational theories for quantum circuits, by getting rid of several rules including a fairly impractical one. One of our main contributions is to prove the minimality of the equational theory, i.e. none of the rules can be derived from the other ones. More generally, we demonstrate that any complete equational theory on quantum circuits (when all gates are unitary) requires rules acting on an unbounded number of qubits. Finally, we also simplify the complete equational theories for quantum circuits with ancillary qubits and/or qubit discarding.
Authors: Alexandre Clément, Noé Delorme, Simon Perdrix
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Paris-Saclay, École Normale Supérieure - PSL, QUACS: Structures de calcul quantique, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Université de Lorraine
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4399889461