ZX-calculus publications

This is intended to be a complete list of all publications that use the ZX-calculus (and related graphical calculi) in some manner. The guiding principle is that if the paper contains at least one ZX-diagram, then it should be in this list. If you find any errors or feel that a missing publication should be included in this list, please contact Richard East or John van de Wetering. If you want to keep up-to-date with additions, there is also an RSS feed.

2021

  • Completeness of the ZH-calculus
    Miriam Backens, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering and Sal Wolffs
    Show abstract ⇲ Show bibdata ⇲ Video 🎥
  • Geometry of Interaction for ZX-Diagrams
    Kostia Chardonnet, Benoit Valiron and Renaud Vilmart
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2020

  • Foundations for Near-Term Quantum Natural Language Processing
    Bob Coecke, Giovanni de Felice, Konstantinos Meichanetzidis and Alexis Toumi
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  • AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
    Richard D. P. East, John van de Wetering, Nicholas Chancellor and Adolfo G. Grushin
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  • Quantum Natural Language Processing on Near-Term Quantum Computers
    Konstantinos Meichanetzidis, Stefano Gogioso, Giovanni de Felice, Nicolò Chiappori, Alexis Toumi and Bob Coecke
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  • There and back again: A circuit extraction tale
    Miriam Backens, Hector Miller-Bakewell, Giovanni de Felice, Leo Lobski and John van de Wetering
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2019

  • Effective Compression of Quantum Braided Circuits Aided by ZX-Calculus
    Michael Hanks, Marta P. Estarellas, William J. Munro and Kae Nemoto
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  • Phase Gadget Synthesis for Shallow Circuits
    Alexander Cowtan, Silas Dilkes, Ross Duncan, Will Simmons and Seyon Sivarajah
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  • Graphical Fourier Theory and the Cost of Quantum Addition
    Stach Kuijpers, John van de Wetering and Aleks Kissinger
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  • Completeness of the ZX-Calculus
    Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart
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  • Completeness of Graphical Languages for Mixed States Quantum Mechanics
    Titouan Carette, Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart
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2018

  • A diagrammatic calculus of fermionic quantum circuits
    Amar Hadzihasanovic, Giovanni de Felice and Kang Feng Ng
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2017

  • Towards a Minimal Stabilizer ZX-calculus
    Miriam Backens, Simon Perdrix and Quanlong Wang
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2016

  • Graphical Structures for Design and Verification of Quantum Error Correction
    Nicholas Chancellor, Aleks Kissinger, Joschka Roffe, Stefan Zohren and Dominic Horsman
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  • A Simplified Stabilizer ZX-calculus
    Miriam Backens, Simon Perdrix and Quanlong Wang
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2015

  • Generalised Compositional Theories and Diagrammatic Reasoning
    Bob Coecke, Ross Duncan, Aleks Kissinger and Quanlong Wang
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2014

2013

2012

2011

  • The GHZ/W-calculus contains rational arithmetic
    Bob Coecke, Aleks Kissinger, Alex Merry and Shibdas Roy
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2010

2009

2008

2007


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