The ZX-calculus Is Complete for Stabilizer Quantum Mechanics

Miriam Backens 2014 The ZX-calculus Is Complete for Stabilizer Quantum Mechanics New Journal of Physics 16 9 093021 10.1088/1367-2630/16/9/093021 Miriam Backens 2015 Making the Stabilizer ZX-calculus Complete for Scalars Chris Heunen Peter Selinger Jamie Vicary Proceedings of the 12th International Workshop on Quantum Physics and Logic Electronic Proceedings in Theoretical Computer Science Open Publishing Association 17–32 10.4204/EPTCS.195.2 Miriam Backens Aleks Kissinger 2019 ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity Peter Selinger Giulio Chiribella Proceedings of the 15th International Conference on Quantum Physics and Logic Electronic Proceedings in Theoretical Computer Science 287 Open Publishing Association

Halifax, Canada

23–42 10.4204/EPTCS.287.2 Miriam Backens Hector Miller-Bakewell Giovanni de Felice Leo Lobski John van de Wetering 2021 There and Back Again: A Circuit Extraction Tale Quantum 5 421 10.22331/q-2021-03-25-421 Miriam Backens Simon Perdrix Quanlong Wang 2017 A Simplified Stabilizer ZX-calculus Ross Duncan Chris Heunen Proceedings 13th International Conference on Quantum Physics and Logic Electronic Proceedings in Theoretical Computer Science 236 Open Publishing Association

Glasgow, Scotland

1–20 10.4204/EPTCS.236.1 Miriam Backens Simon Perdrix Quanlong Wang 2020 Towards a Minimal Stabilizer ZX-calculus Logical Methods in Computer Science Volume 16, Issue 4 10.23638/LMCS-16(4:19)2020 Niel de Beaudrap Xiaoning Bian Quanlong Wang 2020 Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities Steven T. Flammia 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020) Leibniz International Proceedings in Informatics (LIPIcs) 158 Schloss Dagstuhl–Leibniz-Zentrum für Informatik

Dagstuhl, Germany

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Dagstuhl, Germany

24:1–24:15 10.4230/LIPIcs.MFCS.2022.24 Robert I. Booth Titouan Carette 2023 Complete ZX-calculi for the Stabiliser Fragment in Odd Prime Dimensions 2204.12531v3 Earl T. Campbell 2014 Enhanced Fault-Tolerant Quantum Computing in d-Level Systems Physical Review Letters 113 23 230501 10.1103/PhysRevLett.113.230501 1406.3055 Titouan Carette 2021 When Only Topology Matters 2102.03178 Titouan Carette 2021 Wielding the ZX-calculus, Flexsymmetry, Mixed States, and Scalable Notations Loria, Université de Lorraine https://hal.archives-ouvertes.fr/tel-03468027 Yulin Chi Jieshan Huang Zhanchuan Zhang Jun Mao Zinan Zhou Xiaojiong Chen Chonghao Zhai Jueming Bao Tianxiang Dai Huihong Yuan Ming Zhang Daoxin Dai Bo Tang Yan Yang Zhihua Li Yunhong Ding Leif K. Oxenløwe Mark G. Thompson Jeremy L. O'Brien Yan Li Qihuang Gong Jianwei Wang 2022 A Programmable Qudit-Based Quantum Processor Nature Communications 13 1 1166 10.1038/s41467-022-28767-x Julien Codsi John van de Wetering 2023 Classically Simulating Quantum Supremacy IQP Circuits through a Random Graph Approach 2212.08609 Bob Coecke Giovanni de Felice Konstantinos Meichanetzidis Alexis Toumi 2020 Foundations for Near-Term Quantum Natural Language Processing 2012.03755 Bob Coecke Ross Duncan 2008 Interacting Quantum Observables Luca Aceto Ivan Damgård Leslie Ann Goldberg Magnús M. Halldórsson Anna Ingólfsdóttir Igor Walukiewicz Automata, Languages and Programming Lecture Notes in Computer Science Springer

Berlin, Heidelberg

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Paris, France

13–45 10.4204/EPTCS.340.2 Niel de Beaudrap Richard D. P. East 2023 Simple ZX and ZH Calculi for Arbitrary Finite Dimensions, via Discrete Integrals 2304.03310 Niel de Beaudrap Dominic Horsman 2020 The ZX Calculus Is a Language for Surface Code Lattice Surgery Quantum 4 218 10.22331/q-2020-01-09-218 Giovanni de Felice Razin A. Shaikh Boldizsár Poór Lia Yeh Quanlong Wang Bob Coecke 2023 Light-Matter Interaction in the ZXW Calculus 2306.02114 Nadish de Silva 2021 Efficient Quantum Gate Teleportation in Higher Dimensions Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477 2251 20200865 10.1098/rspa.2020.0865 2011.00127 Jeroen Dehaene Bart De Moor 2003 Clifford Group, Stabilizer States, and Linear and Quadratic Operations over GF(2) Physical Review A 68 4 042318 10.1103/PhysRevA.68.042318 quant-ph/0304125 Ross Duncan Aleks Kissinger Simon Perdrix John van de Wetering 2020 Graph-Theoretic Simplification of Quantum Circuits with the ZX-calculus Quantum 4 279 10.22331/q-2020-06-04-279 Ross Duncan Maxime Lucas 2014 Verifying the Steane Code with Quantomatic Bob Coecke Matty Hoban Proceedings of the 10th International Workshop on Quantum Physics and Logic Electronic Proceedings in Theoretical Computer Science 171 Open Publishing Association

Castelldefels (Barcelona), Spain

33–49 10.4204/EPTCS.171.4 Ross Duncan Simon Perdrix 2009 Graph States and the Necessity of Euler Decomposition Klaus Ambos-Spies Benedikt Löwe Wolfgang Merkle Mathematical Theory and Computational Practice Lecture Notes in Computer Science Springer

Berlin, Heidelberg

167–177 10.1007/978-3-642-03073-4_18 Ross Duncan Simon Perdrix 2010 Rewriting Measurement-Based Quantum Computations with Generalised Flow Samson Abramsky Cyril Gavoille Claude Kirchner Friedhelm Meyer auf der Heide Paul G. Spirakis Automata, Languages and Programming Lecture Notes in Computer Science Springer

Berlin, Heidelberg

285–296 10.1007/978-3-642-14162-1_24 Liam Garvie Ross Duncan 2018 Verifying the Smallest Interesting Colour Code with Quantomatic Bob Coecke Aleks Kissinger Proceedings 14th International Conference on Quantum Physics and Logic Electronic Proceedings in Theoretical Computer Science 266 Open Publishing Association

Nijmegen, The Netherlands

147–163 10.4204/EPTCS.266.10 Pranav Gokhale Jonathan M. Baker Casey Duckering Natalie C. Brown Kenneth R. Brown Frederic T. Chong 2019 Asymptotic Improvements to Quantum Circuits via Qutrits Proceedings of the 46th International Symposium on Computer Architecture ISCA '19 Association for Computing Machinery

New York, NY, USA

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Berlin, Heidelberg

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Dagstuhl, Germany

11:1–11:13 10.4230/LIPIcs.MFCS.2017.11 Andrey Boris Khesin Jonathan Z. Lu Peter W. Shor 2023 Graphical Quantum Clifford-encoder Compilers from the ZX Calculus 2301.02356 Aleks Kissinger 2022 Phase-free ZX diagrams are CSS codes (...or how to graphically grok the surface code) 2204.14038 Aleks Kissinger John van de Wetering 2020 PyZX: Large Scale Automated Diagrammatic Reasoning Proceedings 16th International Conference on Quantum Physics and Logic Electronic Proceedings in Theoretical Computer Science 318 Open Publishing Association

CA, USA.

229–241 10.4204/EPTCS.318.14 Aleks Kissinger John van de Wetering 2020 Reducing the Number of Non-Clifford Gates in Quantum Circuits Physical Review A 102 2 022406 10.1103/PhysRevA.102.022406 1903.10477 Aleks Kissinger John van de Wetering Renaud Vilmart 2022 Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions François Le Gall Tomoyuki Morimae 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022) Leibniz International Proceedings in Informatics (LIPIcs) 232 Schloss Dagstuhl Leibniz-Zentrum für Informatik

Dagstuhl, Germany

5:1–5:13 10.4230/LIPIcs.TQC.2022.5 Tuomas Laakkonen Konstantinos Meichanetzidis John van de Wetering 2022 A Graphical #SAT Algorithm for Formulae with Small Clause Density 2212.08048 Tommy McElvanney Miriam Backens 2022 Complete Flow-Preserving Rewrite Rules for MBQC Patterns with Pauli Measurements 2205.02009 Konstantinos Meichanetzidis Stefano Gogioso Giovanni de Felice Nicolò Chiappori Alexis Toumi Bob Coecke 2021 Quantum Natural Language Processing on Near-Term Quantum Computers Benoît Valiron Shane Mansfield Pablo Arrighi Prakash Panangaden Proceedings 17th International Conference on Quantum Physics and Logic Electronic Proceedings in Theoretical Computer Science 340 Open Publishing Association

Paris, France

213–229 10.4204/EPTCS.340.11 A. S. Nikolaeva E. O. Kiktenko A. K. Fedorov 2022 Decomposing the Generalized Toffoli Gate with Qutrits Physical Review A 105 3 032621 10.1103/PhysRevA.105.032621 2112.14535 Simon Perdrix Quanlong Wang 2016 Supplementarity Is Necessary for Quantum Diagram Reasoning Piotr Faliszewski Anca Muscholl Rolf Niedermeier 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) Leibniz International Proceedings in Informatics (LIPIcs) 58 Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik

Dagstuhl, Germany

76:1–76:14 10.4230/LIPIcs.MFCS.2016.76 Boldizsár Poór Quanlong Wang Razin A. Shaikh Lia Yeh Richie Yeung Bob Coecke 2023 Completeness for Arbitrary Finite Dimensions of ZXW-calculus, a Unifying Calculus 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

Boston, MA, USA

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Kyoto, Japan

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Nijmegen, The Netherlands

58–70 10.4204/EPTCS.266.3 Quanlong Wang 2022 Qufinite ZX-calculus: A Unified Framework of Qudit ZX-calculi 2104.06429 Quanlong Wang Richie Yeung Mark Koch 2022 Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning 2201.13250 Yuchen Wang Zixuan Hu Barry C. Sanders Sabre Kais 2020 Qudits and High-Dimensional Quantum Computing Frontiers in Physics 8 10.3389/fphy.2020.589504 Biaoliang Ye Zhen-Fei Zheng Yu Zhang Chui-Ping Yang 2018 Circuit QED: single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling n-1 microwave photonic qubits Optics Express 26 23 30689–30702 10.1364/OE.26.030689 Lia Yeh John van de Wetering 2022 Constructing All Qutrit Controlled Clifford+T Gates in Clifford+T Claudio Antares Mezzina Krzysztof Podlaski Reversible Computation Lecture Notes in Computer Science Springer International Publishing

Cham

28–50 10.1007/978-3-031-09005-9_3 2204.00552 M. A. Yurtalan J. Shi M. Kononenko A. Lupascu S. Ashhab 2020 Implementation of a Walsh-Hadamard Gate in a Superconducting Qutrit Physical Review Letters 125 18 180504 10.1103/PhysRevLett.125.180504 2003.04879 Yutsumura 2017 Each Element in a Finite Field Is the Sum of Two Squares https://yutsumura.com/each-element-in-a-finite-field-is-the-sum-of-two-squares Fabio Zanasi 2018 Interacting Hopf Algebras: The Theory of Linear Systems Ecole Normale Superieure de Lyon 1805.03032 Chen Zhao Xiao-Shan Gao 2021 Analyzing the Barren Plateau Phenomenon in Training Quantum Neural Networks with the ZX-calculus Quantum 5 466 10.22331/q-2021-06-04-466