Work

Controlled PROP: Theory and Applications to Quantum Circuits

Year: 2026

Type: preprint

Abstract: Control is a fundamental concept in quantum and reversible computational models. It enables the conditional application of a transformation to a system, depending on the state of another system. We introduce a general framework for diagrammatic reasoning featuring control as a constructor. To this end, we provide an elementary axiomatization of control functors, extending the standard formalism of PROPs to controlled PROPs. As an application, we show that controlled PROPs facilitate diagrammatic reasoning for quantum circuits. In particular, they admit a simple and complete axiomatization involving at most three qubits, whereas in the standard PROP setting, completeness necessarily requires axioms involving arbitrarily many qubits.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.23192

Authors: Delorme, Noé, Perdrix, Simon

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

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Agence Nationale de la Recherche

Awards: Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l’informatique quantique, Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés

OpenAlex ID: W7222976126

Cites: 26

Cited by:

Related to: 10