Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2508.21756 · Lecture notes in computer science

Diagrammatic Reasoning with Control as a Constructor, Applications to Quantum Circuits

Noé Delorme, Simon Perdrix

Published Jan 1, 2026• 1 citation
arXivHTMLPDF
DOI
10.1007/978-3-032-22730-0_12

Related papers

Topological-Like Features in Diagrammatical Quantum Circuits

Yong Zhang, Louis Hirsch Kauffman

arXiv:quant-ph/0703196•Quantum Information Processing•Dec 6, 2007•4 citations

Controlled PROP: Theory and Applications to Quantum Circuits

Noé Delorme, Simon Perdrix

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.

quant-pharXiv:2610.23192•Oct 19, 2026•0 citations

Algebraic and Logical Emulations of Quantum Circuits

Kenneth W. Regan, Amlan Chakrabarti, Chaowen Guan

Lecture notes in computer science•Jan 1, 2018•1 citation

Quantum Computational Logics: A Survey

María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini

arXiv:quant-ph/0305029•Trends in logic•Jan 1, 2003•47 citations

PyZX: Large Scale Automated Diagrammatic Reasoning

Aleks Kissinger, John van de Wetering

The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we can intuitively reason about quantum theory, and optimise and validate quantum circuits. In this paper we introduce PyZX, an open source library for automated reasoning with large ZX-diagrams. We give a brief introduction to the ZX-calculus, then show how PyZX implements methods for circuit optimisation, equality validation, and visualisation and how it can be used in tandem with other software. We end with a set of challenges that when solved would enhance the utility of automated diagrammatic reasoning.

arXiv:1904.04735•Electronic Proceedings in Theoretical Computer Science•Apr 30, 2020•159 citations

Applications of a Circuit QED Quantum Channel Constructor

Chao Shen, Kyungjoo Noh, Victor V. Albert +5 more

Bulletin of the American Physical Society•Mar 16, 2017•0 citations
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.
The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we can intuitively reason about quantum theory, and optimise and validate quantum circuits. In this paper we introduce PyZX, an open source library for automated reasoning with large ZX-diagrams. We give a brief introduction to the ZX-calculus, then show how PyZX implements methods for circuit optimisation, equality validation, and visualisation and how it can be used in tandem with other software. We end with a set of challenges that when solved would enhance the utility of automated diagrammatic reasoning.