ZX-calculus publications

2019

  • Phase Gadget Synthesis for Shallow Circuits, Alexander Cowtan, Silas Dilkes, Ross Duncan, Will Simmons and Seyon Sivarajah, arXiv preprint arXiv:1906.01734 (2019).
    Keywords: Phase Gadget, Chemistry, ZX-calculus. Abstract   Bibdata
  • SZX-calculus: Scalable Graphical Quantum Reasoning, Titouan Carette, Dominic Horsman and Simon Perdrix, arXiv preprint arXiv:1905.00041 (2019).
    Keywords: ZX-calculus, Scalable ZX. Abstract   Bibdata
  • Hopf-Frobenius algebras and a new Drinfeld double, Joseph Collins and Ross Duncan, arXiv preprint arXiv:1905.00797 (2019).
    Keywords: Frobenius algebras, Category Theory. Abstract   Bibdata
  • PyZX: Large Scale Automated Diagrammatic Reasoning, Aleks Kissinger and John van de Wetering, arXiv preprint arXiv:1904.04735 (2019).
    Keywords: ZX-Calculus, Circuit Optimisation, PyZX, Automation. Abstract   Bibdata
  • Completeness of the Phase-free ZH-calculus, John van de Wetering and Sal Wolffs, arXiv preprint arXiv:1904.07545 (2019).
    Keywords: ZH-Calculus, Completeness. Abstract   Bibdata
  • Graphical Fourier Theory and the Cost of Quantum Addition, Stach Kuijpers, John van de Wetering and Aleks Kissinger, arXiv preprint arXiv:1904.07551 (2019).
    Keywords: ZH-Calculus, ZX-Calculus, Fourier. Abstract   Bibdata
  • CNOT circuit extraction for topologically-constrained quantum memories, Aleks Kissinger and Arianne Meijer-van de Griend, arXiv preprint arXiv:1904.00633 (2019).
    Keywords: ZX Adjacent, CNOT, Circuit extraction, Quantum memories. Abstract   Bibdata
  • Pauli Fusion: a computational model to realise quantum transformations from ZX terms, Niel de Beaudrap, Ross Duncan, Dominic Horsman and Simon Perdrix, arXiv preprint arXiv:1904.12817 (2019).
    Keywords: ZX-calculus, Lattice Surgery, Pauli Fusion. Abstract   Bibdata
  • Finite Verification for Infinite Families of Diagram Equations, Hector Miller-Bakewell, arXiv preprint arXiv:1904.00706 (2019).
    Keywords: ZX-calculus, Bang-Boxes, ZH-calculus, ZW-calculus, Automation. Abstract   Bibdata
  • Completeness of the ZX-Calculus, Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, arXiv preprint arXiv:1903.06035 (2019).
    Keywords: ZX-Calculus, Completeness, Triangle, Clifford+T, Universal Fragment. Abstract   Bibdata
  • Reducing T-count with the ZX-calculus, Aleks Kissinger and John van de Wetering, arXiv preprint arXiv:1903.10477 (2019).
    Keywords: ZX-Calculus, Clifford+T, Circuit Optimisation. Abstract   Bibdata
  • Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus, Ross Duncan, Aleks Kissinger, Simon Pedrix and John van de Wetering, arXiv preprint arXiv:1902.03178 (2019).
    Keywords: ZX-Calculus, Circuit optimisation. Abstract   Bibdata
  • Completeness of Graphical Languages for Mixed States Quantum Mechanics, Titouan Carette, Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, arXiv:1902.07143 [quant-ph] (2019).
    Keywords: Completeness, Category Theory, Mixed States. Abstract   Bibdata
  • Optimising Clifford Circuits with Quantomatic, Andrew Fagan and Ross Duncan, Proceedings of the 15th International Conference on Quantum Physics and Logic (QPL) (2019).
    Keywords: ZX-Calculus, Quantomatic, Clifford Fragment, Circuit optimisation, Automation. Abstract   Bibdata

2018

  • A Near-Optimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum Mechanics, Renaud Vilmart, arXiv preprint arXiv:1812.09114 (2018).
    Keywords: ZX-Calculus, Completeness, Universal Fragment. Abstract   Bibdata
  • The rational fragment of the ZX-calculus, Emmanuel Jeandel, arXiv:1810.05377 [quant-ph] (2018).
    Keywords: ZX-Calculus, Rational Fragment, Completeness. Abstract   Bibdata
  • A Generic Normal Form for ZX-Diagrams and Application to the Rational Angle Completeness, Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, arXiv preprint arXiv:1805.05296 (2018).
    Keywords: ZX-Calculus, Normal-form, Rational Fragment. Abstract   Bibdata
  • ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity, Miriam Backens and Aleks Kissinger, Proceedings of the 15th International Conference on Quantum Physics and Logic, Halifax, Canada, 3-7th June 2018 (2019).
    Keywords: ZH-calculus, Completeness. Abstract   Bibdata
  • ZX-rules for 2-qubit Clifford+ T quantum circuits, Bob Coecke and Quanlong Wang, International Conference on Reversible Computation (2018).
    Keywords: ZX-Calculus, Completeness, Clifford+T. Abstract   Bibdata
  • A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond, Renaud Vilmart, Proceedings of the 15th International Conference on Quantum Physics and Logic, Halifax, Canada, 3-7th June 2018 (2019).
    Keywords: ZX-Calculus, Completeness, Triangle. Abstract   Bibdata
  • Qutrit ZX-calculus is Complete for Stabilizer Quantum Mechanics, Quanlong Wang, Proceedings 14th International Conference on Quantum Physics and Logic, Nijmegen, The Netherlands, 3-7 July 2017 (2018).
    Keywords: ZX-Calculus, Qutrits, Clifford Fragment. Abstract   Bibdata
  • Diagrammatic Reasoning Beyond Clifford+T Quantum Mechanics, Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (2018).
    Keywords: ZX-Calculus, Completeness, Universal Fragment. Abstract   Bibdata
  • A Diagrammatic Axiomatisation of Fermionic Quantum Circuits, Amar Hadzihasanovic, Giovanni de Felice and Kang Feng Ng, 3rd International Conference on Formal Structures for Computation and Deduction (2018).
    Keywords: ZW-Calculus, Completeness, Fermionic quantum computing. Abstract   Bibdata
  • Completeness of the ZX-calculus for Pure Qubit Clifford+T Quantum Mechanics, Kang Feng Ng and Quanlong Wang, arXiv:1801.07993 [quant-ph] (2018).
    Keywords: ZX-Calculus, Completeness, Clifford+T. Abstract   Bibdata
  • Two Complete Axiomatisations of Pure-state Qubit Quantum Computing, Amar Hadzihasanovic, Kang Feng Ng and Quanlong Wang, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (2018).
    Keywords: ZW-Calculus, Completeness, Universal Fragment, Normal-form. Abstract   Bibdata
  • Completeness of the ZX-calculus, Quanlong Wang, PhD Thesis (2018).
    Keywords: ZX-Calculus, Completeness, PhD Thesis. Abstract   Bibdata
  • Towards Minimality of Clifford+T ZX-Calculus, Borun Shi, University of Oxford Master thesis (2018).
    Keywords: ZX-Calculus, Minimality, Master Thesis. Abstract   Bibdata

2017

  • The algebra of entanglement and the geometry of composition, Amar Hadzihasanovic, PhD Thesis (2017).
    Keywords: ZW-Calculus, Completeness, PhD Thesis. Abstract   Bibdata
  • A universal completion of the ZX-calculus, Kang Feng Ng and Quanlong Wang, arXiv preprint arXiv:1706.09877 (2017).
    Keywords: ZX-Calculus, Completeness, Universal Fragment. Abstract   Bibdata
  • Verifying the Smallest Interesting Colour Code with Quantomatic, Liam Garvie and Ross Duncan, Proceedings 14th International Conference on Quantum Physics and Logic, Nijmegen, The Netherlands, 3-7 July 2017 (2018).
    Keywords: ZX-Calculus, Quantomatic, Error correcting codes. Abstract   Bibdata
  • A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics, Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (2018).
    Keywords: Clifford+T, Completeness, ZX-Calculus. Abstract   Bibdata
  • Universal MBQC with generalised parity-phase interactions and Pauli measurements, Aleks Kissinger and John van de Wetering, Quantum (2019).
    Keywords: ZX-Calculus, Clifford+T, MBQC. Abstract   Bibdata
  • The ZX calculus is a language for surface code lattice surgery, Niel de Beaudrap and Dominic Horsman, arXiv preprint arXiv:1704.08670 (2017).
    Keywords: ZX-Calculus, Lattice Surgery, Topological Quantum Computing. Abstract   Bibdata
  • Equivalence of Local Complementation and Euler Decomposition in the Qutrit ZX-calculus, Xiaoyan Gong and Quanlong Wang, arXiv:1704.05955 [quant-ph] (2017).
    Keywords: ZX-Calculus, Qutrits, Local Complementation. Abstract   Bibdata
  • Categorifying the ZX-calculus, Daniel Cicala, Proceedings 14th International Conference on Quantum Physics and Logic, Nijmegen, The Netherlands, 3-7 July 2017 (2018).
    Keywords: ZX-Calculus, Category Theory. Abstract   Bibdata
  • ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics, Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart and Quanlong Wang, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) (2017).
    Keywords: ZX-Calculus, Completeness, Rational Fragment. Abstract   Bibdata
  • Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus, Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart, Proceedings 14th International Conference on Quantum Physics and Logic, Nijmegen, The Netherlands, 3-7 July 2017 (2018).
    Keywords: Y-Calculus, Completeness, Real Fragment. Abstract   Bibdata
  • Picturing Quantum Processes, Bob Coecke and Aleks Kissinger, Cambridge University Press (2017).
    Keywords: . Abstract   Bibdata

2016

  • Graphical Structures for Design and Verification of Quantum Error Correction, Nicholas Chancellor, Aleks Kissinger, Joschka Roffe, Stefan Zohren and Dominic Horsman, arXiv preprint arXiv:1611.08012 (2016).
    Keywords: ZX-Calculus, Quantomatic, Error correcting codes. Abstract   Bibdata
  • A Simplified Stabilizer ZX-calculus, Miriam Backens, Simon Perdrix and Quanlong Wang, Proceedings 13th International Conference on Quantum Physics and Logic, Glasgow, Scotland, 6-10 June 2016 (2017).
    Keywords: ZX-Calculus, Completeness, Clifford Fragment. Abstract   Bibdata
  • Completeness and the ZX-calculus, Miriam Backens, PhD Thesis (2016).
    Keywords: ZX-Calculus, Completeness, PhD Thesis. Abstract   Bibdata

2015

  • Making the stabilizer ZX-calculus complete for scalars, Miriam Backens, Proceedings of the 12th International Workshop on Quantum Physics and Logic (QPL 2015) (2015).
    Keywords: ZX-Calculus, Completeness, Scalars. Abstract   Bibdata
  • Supplementarity is Necessary for Quantum Diagram Reasoning, Simon Perdrix and Quanlong Wang, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) (2016).
    Keywords: ZX-Calculus, Completeness, Clifford+T. Abstract   Bibdata
  • Quantomatic: A proof assistant for diagrammatic reasoning, Aleks Kissinger and Vladimir Zamdzhiev, International Conference on Automated Deduction (2015).
    Keywords: Quantomatic, Automation. Abstract   Bibdata
  • A diagrammatic axiomatisation for qubit entanglement, Amar Hadzihasanovic, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (2015).
    Keywords: ZW-Calculus, Completeness. Abstract   Bibdata

2014

  • The ZX-calculus is complete for the single-qubit Clifford+T group, Miriam Backens, Proceedings of the 11th workshop on Quantum Physics and Logic, Kyoto, Japan, 4-6th June 2014 (2014).
    Keywords: ZX-Calculus, Clifford+T, Completeness. Abstract   Bibdata
  • A Complete Graphical Calculus for Spekkens’ Toy Bit Theory, Miriam Backens and Ali Nabi Duman, Foundations of Physics (2015).
    Keywords: ZX-Calculus, Spekkens Toy Model, Completeness. Abstract   Bibdata
  • Qutrit Dichromatic Calculus and Its Universality, Quanlong Wang and Xiaoning Bian, Electronic Proceedings in Theoretical Computer Science (2014).
    Keywords: ZX-Calculus, Qutrit, Qudit. Abstract   Bibdata
  • The ZX-calculus is incomplete for quantum mechanics, Christian Schröder de Witt and Vladimir Zamdzhiev, Proceedings QPL 2014 (2014).
    Keywords: ZX-Calculus, Completeness. Abstract   Bibdata
  • Depicting qudit quantum mechanics and mutually unbiased qudit theories, André Ranchin, Proceedings of the 11th workshop on Quantum Physics and Logic, Kyoto, Japan, 4-6th June 2014 (2014).
    Keywords: ZX-calculus, Qudits, Spekkens Toy Model. Abstract   Bibdata

2013

  • Complete set of circuit equations for stabilizer quantum mechanics, André Ranchin and Bob Coecke, Physical Review A (2014).
    Keywords: ZX-Calculus, Completeness, Clifford Fragment. Abstract   Bibdata
  • Pivoting makes the ZX-calculus complete for real stabilizers, Ross Duncan and Simon Perdrix, Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL) (2014).
    Keywords: ZX-Calculus, Clifford Fragment, Completeness. Abstract   Bibdata
  • The ZX-calculus is complete for stabilizer quantum mechanics, Miriam Backens, New Journal of Physics (2014).
    Keywords: ZX-Calculus, Completeness, Clifford Fragment, Normal-form. Abstract   Bibdata
  • Verifying the Steane code with Quantomatic, Ross Duncan and Maxime Lucas, Proceedings of the 10th International Workshop on Quantum Physics and Logic, Castelldefels (Barcelona), Spain, 17th to 19th July 2013 (2014).
    Keywords: ZX-Calculus, Quantomatic, Error correcting codes. Abstract   Bibdata
  • The ZX calculus is incomplete for non-stabilizer quantum mechanics, Christian Schröder de Witt, University of Oxford Master thesis (2013).
    Keywords: ZX-Calculus, Completeness, Master Thesis. Abstract   Bibdata

2012

  • Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus, Anne Hillebrand, Electronic Proceedings in Theoretical Computer Science (2012).
    Keywords: ZX-Calculus, Protocols. Abstract   Bibdata
  • Strong complementarity and non-locality in categorical quantum mechanics, Bob Coecke, Ross Duncan, Aleks Kissinger and Quanlong Wang, Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science (LICS) (2012).
    Keywords: Foundational, Category Theory. Abstract   Bibdata
  • A graphical approach to measurement-based quantum computing, Ross Duncan, arXiv preprint arXiv:1203.6242 (2013).
    Keywords: ZX-calculus, MBQC. Abstract   Bibdata

2011

  • Trichromatic Open Digraphs for Understanding Qubits, Alex Lang and Bob Coecke, Proceedings 8th International Workshop on Quantum Physics and Logic, Nijmegen, Netherlands, October 27-29, 2011 (2012).
    Keywords: ZX-Calculus. Abstract   Bibdata
  • Three qubit entanglement within graphical Z/X-calculus, Bob Coecke and Bill Edwards, Proceedings CSR 2010 Workshop on High Productivity Computations, Kazan, Russia, June 21-22, 2010 (2011).
    Keywords: ZX-Calculus, Entanglement, ZW-Calculus. Abstract   Bibdata
  • The GHZ/W-calculus contains rational arithmetic, Bob Coecke, Aleks Kissinger, Alex Merry and Shibdas Roy, Electronic Proceedings in Theoretical Computer Science (2010).
    Keywords: ZW-Calculus, Foundational. Abstract   Bibdata
  • Quantum picturalism for topological cluster-state computing, Clare Horsman, New Journal of Physics (2011).
    Keywords: ZX-calculus, Topological Quantum Computing. Abstract   Bibdata
  • Quantum Protocols involving Multiparticle Entanglement and their Representations in the ZX-calculus, Anne Hillebrand, University of Oxford Master thesis (2011).
    Keywords: ZX-Calculus, Protocols, Master Thesis. Abstract   Bibdata
  • Towards normal forms for GHZ/W calculus, Shibdas Roy, AIP Conference Proceedings (2011).
    Keywords: ZW-calculus, Normal-forms. Abstract   Bibdata

2010

  • Environment and classical channels in categorical quantum mechanics, Bob Coecke and Simon Perdrix, Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL) (2010).
    Keywords: ZX-Calculus, Foundational. Abstract   Bibdata
  • Phase groups and the origin of non-locality for qubits, Bob Coecke, Bill Edwards and Rob Spekkens, Electronic Notes in Theoretical Computer Science (2011).
    Keywords: ZX-Calculus, Spekkens Toy Model. Abstract   Bibdata
  • The compositional structure of multipartite quantum entanglement, Bob Coecke and Aleks Kissinger, Automata, Languages and Programming (2010).
    Keywords: ZW-Calculus, Foundational. Abstract   Bibdata
  • Rewriting measurement-based quantum computations with generalised flow, Ross Duncan and Simon Perdrix, International Colloquium on Automata, Languages, and Programming (2010).
    Keywords: ZX-Calculus, MBQC. Abstract   Bibdata
  • Models of Multipartite Entanglement, Michael Herrmann, University of Oxford Master thesis (2010).
    Keywords: ZW-Calculus, Entanglement, Master Thesis. Abstract   Bibdata

2009

  • Quantum picturalism, Bob Coecke, Contemporary Physics (2009).
    Keywords: ZX-Calculus, Foundational. Abstract   Bibdata
  • Interacting quantum observables: categorical algebra and diagrammatics, Bob Coecke and Ross Duncan, New Journal of Physics (2011).
    Keywords: ZX-Calculus, Foundational. Abstract   Bibdata
  • Graph states and the necessity of Euler decomposition, Ross Duncan and Simon Perdrix, Conference on Computability in Europe (2009).
    Keywords: ZX-Calculus, Clifford Fragment, Graph-states, Foundational. Abstract   Bibdata

2008

  • Interacting quantum observables, Bob Coecke and Ross Duncan, Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP) (2008).
    Keywords: ZX-Calculus, Foundational. Abstract   Bibdata

Home Tutorial Publications Accessibility Map PyZX Demo