Year: 2023
Type: conference-paper
Abstract: We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations. The proof is based on the properties of multi-controlled gates – that are defined using elementary gates – together with an encoding of quantum circuits into linear optical circuits, which have been proved to have a complete axiomatisation.
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Université de Lorraine, Quandela (France), Université Paris-Saclay, CentraleSupélec, Laboratoire Méthodes Formelles
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4283323927