PreprintCC BY 4.0arXiv
Controlled PROP: Theory and Applications to Quantum Circuits
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.
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BibTeX
@misc{delorme2026controlled,
title = {{Controlled PROP: Theory and Applications to Quantum Circuits}},
author = {Noé Delorme and Simon Perdrix},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23192},
eprint = {2610.23192},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23192},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Controlled PROP: Theory and Applications to Quantum Circuits
AU - Noé Delorme
AU - Simon Perdrix
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23192
UR - https://arxiv.org/abs/2610.23192
AB - 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.
ER -