# Aleks Kissinger

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## Publications

The following is a list of all of my publications, ordered by year, along with links to published versions and arXiv preprint, where available. Some open-access publications (e.g. EPTCS) publish directly via arXiv, in which case a single link is provided.

Citations for most papers below are also available as bibtex.

### 2023

*Quantum Picturalism: Learning Quantum Theory in High School*. Selma Dündar-Coecke, Lia Yeh, Caterina Puca, Sieglinde M.-L. Pfaendler, Muhammad Hamza Waseem, Thomas Cervoni, Aleks Kissinger, Stefano Gogioso, Bob Coecke. In proceedings of Quantum Science and Engineering Education Conference, IEEE International Conference on Quantum Computing and Engineering 2023.*Graphical Structures for Design and Verification of Quantum Error Correction*. Nicholas Chancellor, Dominic Horsman, Aleks Kissinger, Joshua Roffe, Stefan Zohren. Quantum Science and Technology. arXiv*Global Synthesis of CNOT Circuits with Holes*. Ewan Murph, Aleks Kissinger. In proceedings of the 20th International Conference of Quantum Physics and Logic (QPL) 2023. arXiv*Graphical CSS Code Transformation using the ZX Calculus*. Jiaxin Huang, Sarah Meng Li, Lia Yeh, Aleks Kissinger, Michele Mosca, Michael Vasmer. In proceedings of the 20th International Conference of Quantum Physics and Logic (QPL) 2023. arXiv*The ZX-Calculus as a Language for Topological Quantum Computation*. Fatimah Ahmadi, Aleks Kissinger. Journal of Physics A. arXiv*Completeness of the ZH Calculus*. Miriam Backens, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering, Sal Wolffs. Compositionality 5, 2023. published version

### 2022

*Outcome-determinism for Measurement-based Quantum Computation with Qudits*. Robert Booth, Aleks Kissinger, Damian Markham, Clement Meignant, Simon Perdrix. Journal of Physics A, 2022.*Phase-free ZX diagrams are CSS codes (...or how to graphically grok the surface code)*. Aleks Kissinger. Proceedings 19th International Conference on Quantum Physics and Logic (QPL). arXiv | YouTube*On the pre- and promonoidal structure of spacetime.*James Hefford, Aleks Kissinger. Proceedings 19th International Conference on Quantum Physics and Logic (QPL). arXiv*Quantum Supermaps are Characterized by Locality.*Matt Wilson, Giulio Chiribella, Aleks Kissinger. Preprint. arXiv*The CBH characterisation theorem beyond algebraic quantum theory*. Aleks Kissinger and Chris Heunen. Information and Computation. published version | arXiv*String Diagram Rewrite Theory I: Rewriting with Frobenius Structure.*Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasi. Journal of the Association for Computing Machinery (J. ACM 69(2)). published version | arXiv*Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions*. Aleks Kissinger, John van de Wetering, and Renaud Vilmart. 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC). published version | arXiv*Circuit Extraction for ZX-diagrams can be #P-hard.*Niel de Beaudrap, Aleks Kissinger, John van de Wetering. 49th International Colloquium on Automata, Languages, and Programming (ICALP). published version | arXiv*Higher-Order Causal Theories Are Models of BV-Logic.*Will Simmons, Aleks Kissinger. Proceedings of the 47th International Symposium on Mathematical Foundations of Computer Science (MFCS). published version | arXiv*Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus).*Bob Coecke, Dominic Horsman, Aleks Kissinger, Quanlong Wang. Theoretical Computer Science, Elsevier 2022. published version | arXiv

### 2021

*Outcome determinism in measurement-based quantum computation with qudits.*Robert I. Booth, Aleks Kissinger, Damian Markham, Clément Meignant, Simon Perdrix. arXiv*Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions.*Aleks Kissinger, John van de Wetering. arXiv*A Graphical Calculus for Lagrangian Relations.*Cole Comfort, Aleks Kissinger. Proceedings of the 3rd Conference on Applied Category Theory. 2021. arXiv*String Diagram Rewrite Theory III: Confluence with and without Frobenius.*Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Paweł Sobociński, Fabio Zanasi. arXiv*String Diagram Rewrite Theory II: Rewriting with Symmetric Monoidal Structure.*Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasi. arXiv*Completeness of the ZH-calculus.*Miriam Backens, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering, Sal Wolffs. arXiv

### 2020

*Reducing the number of non-Clifford gates in quantum circuits*. Aleks Kissinger, John van de Wetering. Phys. Rev. A 102, 022406. published version | arXiv*CNOT circuit extraction for topologically-constrained quantum memories*. Aleks Kissinger, Arianne Meijer-van de Griend. Quantum Information and Computation 20, 8. published version | arXiv*Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus*. Ross Duncan, Aleks Kissinger, Simon Perdrix, John van de Wetering. Quantum 4, 279. Quantum page | arXiv*Hypergraph simplification: Linking the path-sum approach to the ZH-calculus*. Louis Lemonnier, Aleks Kissinger and John van de Wetering. In proceedings of the 17th International Conference on Quantum Physics and Logic (QPL). published version | arXiv*Tensor Network Rewriting Strategies for Satisfiability and Counting*. Niel de Beaudrap, Aleks Kissinger, Konstantinos Meichanetzidis. In proceedings of the 17th International Conference on Quantum Physics and Logic (QPL). published version | arXiv

### 2019

*A categorical semantics for causal structure (journal version).*Aleks Kissinger, Sander Uijlen. Logical Methods in Computer Science (LMCS) Vol. 15 (3). published version | arXiv*Graphical Fourier Theory and the Cost of Quantum Addition*. Stach Kuijpers, John van de Wetering, Aleks Kissinger. arXiv*PyZX: Large Scale Automated Diagrammatic Reasoning*. Aleks Kissinger, John van de Wetering. In proceedings of the 16th International Conference on Quantum Physics and Logic (QPL). arXiv*Universal MBQC with generalised parity-phase interactions and Pauli measurements*. Aleks Kissinger and John van de Wetering. Quantum 3, 134. Quantum page | arXiv*Causal Inference by String Diagram Surgery*. Bart Jacobs, Aleks Kissinger, Fabio Zanasi. In proceedings of the International Conference on Foundations of Software Science and Computation Structures (FOSSACS 2019). published version | arXiv

### 2018

*ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity*. Miriam Backens, Aleks Kissinger. In proceedings of the 15th Annual Conference of Quantum Physics and Logic (QPL). published version | arXiv*Rewriting with Frobenius*. Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasi. In proceedings of the 33rd Annual ACM/IEEE symposium on Logic in Computer Science (LICS). published version*Globular: an online proof assistant for higher-dimensional rewriting (journal version)*. Krzysztof Bar, Aleks Kissinger, Jamie Vicary. Logical Methods in Computer Science (LMCS) Vol. 14(1:8). published version

### 2017

*Picture-perfect Quantum Key Distribution*. Aleks Kissinger, Sean Tull, and Bas Westerbaan. arXiv*Equivalence of relativistic causal structure and process terminality.*Bob Coecke, Matty Hoban, and Aleks Kissinger. arXiv*Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem*. Stefano Gogioso and Aleks Kissinger. arXiv*A categorical semantics for causal structure.*Aleks Kissinger and Sander Uijlen. In proceedings of the 32nd Annual ACM/IEEE symposium on Logic in Computer Science (LICS) 2017. published version*Confluence of graph rewriting with interfaces.*Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasi. In proceedings of the 26th European Symposium on Programming (ESOP) 2017. published versionofficial website*Picturing Quantum Processes: A first course in quantum theory and diagrammatic reasoning.*Bob Coecke and Aleks Kissinger. Cambridge University Press. 2017.

### 2016

*Picturing Indefinite Causal Structure.*Aleks Kissinger, Sander Uijlen. In proceedings of the 13th conference on Quantum Physics and Logic (QPL). published version (EPTCS)*Rewriting modulo symmetric monoidal structure.*Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasi. In proceedings of the 31st Annual ACM/IEEE symposium on Logic in Computer Science (LICS) 2016. published version | arXiv*Globular: an online proof assistant for higher-dimensional rewriting.*Krzysztof Bar, Aleks Kissinger, Jamie Vicary. In proceedings of the 1st International Conference on Formal Structures for Computation and Deduction (FSCD) 2016. published version | arXiv*Tensors, !-graphs, and non-commutative quantum structures (extended version).*Aleks Kissinger and David Quick. Next Generation Computing 34(1). Springer/Ohmsha 2016. published version | arXiv*Categorical Quantum Mechanics II: Classical-Quantum Interaction.*Bob Coecke and Aleks Kissinger. In International Jounal of Quantum Information. Vol. 14, Issue 4. World Scientific 2016. published version | arXiv*Categorical Quantum Mechanics I: Causal Quantum Processes.*Bob Coecke and Aleks Kissinger. In Categories for the Working Philosopher. Oxford University Press arXiv

### 2015

*Generalised Compositional Theories and Diagrammatic Reasoning.*Bob Coecke, Ross Duncan, Aleks Kissinger, and Quanlong Wang. In Quantum Theory: Informational Foundations and Foils. Springer Fundamental Theories of Physics vol. 181. 2015. published version | arXiv*A first-order logic for string diagrams.*Aleks Kissinger and David Quick. In proceedings of the 6th Conference on Algebra and Coalgebra (CALCO) 2015. published version | arXiv*Equational reasoning with context-free families of string diagrams.*Aleks Kissinger and Vladimir Zamdzhiev. In proceedings of the International Conference on Graph Transformation (ICGT) 2015. published version | arXiv*Quantomatic: A proof assistant for diagrammatic reasoning.*Aleks Kissinger and Vladimir Zamdzhiev. In proceedings of the 25th International Conference on Automated Deduction (CADE) 2015. published version | arXiv*!-Graphs with trivial overlap are context-free.*Aleks Kissinger and Vladimir Zamdzhiev. In proceedings of Graphs as Models (GaM), workshop at ETAPS, 2015. published version (EPTCS)

### 2014

*Tensors, !-graphs, and non-commutative quantum structures.*Aleks Kissinger and David Quick. In proceedings of the 11th workshop on Quantum Physics and Logic (QPL) 2014. published version (EPTCS)*Tinker, Tailor, Solver, Proof.*Gudmund Grov, Aleks Kissinger, and Yuhui Lin. In proceedings of User Interfaces for Theorem Proving (UITP), workshop at FLoC, Vienna Summer of Logic, 2014. published version (EPTCS)*Categories of Quantum and Classical Channels.*Bob Coecke, Chris Heunen, Aleks Kissinger. Quantum Information Processing, Springer 2014. published version | arXiv

### 2013

*A Graphical Language for Proof Strategies.*Gudmund Grov, Aleks Kissinger, and Yuhui Lin. In proceedings of the 19th International Conference of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR). Springer LNCS 8312. 2013. published version | arXiv*Completely Positive Projections and Biproducts.*Chris Heunen, Aleks Kissinger, Peter Selinger. In proceedings of the 10th workshop on Quantum Physics and Logic (QPL) 2013. published version (EPTCS)*Abstract Tensor Systems as Monoidal Categories.*Aleks Kissinger. In Categories and Types in Logic, Language, and Physics, Essays dedicated to Jim Lambek on the Occasion of this 90th Birthday. Springer LNCS 8222. 2013. published version | arXiv*Compositional Quantum Logic.*Bob Coecke, Chris Heunen, Aleks Kissinger. In Computation, Logic, Games, and Quantum Foundations: The Many Facets of Samson Abramsky. Springer LNCS 7860. 2013. published version | arXiv

### 2012

*Categories of Quantum and Classical Channels (extended abstract).*Bob Coecke, Chris Heunen, Aleks Kissinger. In proceedings of the 9th workshop on Quantum Physics and Logic (QPL) 2012. published version (EPTCS)*Pattern Graph Rewrite Systems.*Alex Merry, Aleks Kissinger, Matvey Soloviev. In proceedings of the 8th workshop on Developments in Computational Models (DCM) 2012. published version (EPTCS)*Synthesising Graphical Theories.*Aleks Kissinger. In proceedings of the workshop on Automated Theory eXploration (ATX) 2012. published version | arXiv*Strong Complementarity and Non-locality in Categorical Quantum Mechanics.*Bob Coecke, Ross Duncan, Aleks Kissinger, Quanlong Wang. In proceedings of the 27th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) 2012. published version | arXiv**PHD THESIS: Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing.**arXiv

### 2011 and earlier

*The GHZ/W-Calculus Contains Rational Arithmetic.*Bob Coecke, Aleks Kissinger, Alex Merry, and Shibdas Roy. In proceedings CSR 2010 Workshop on High Productivity Computations. published version (EPTCS)*The Compositional Structure of Multipartite Quantum Entanglement.*Bob Coecke and Aleks Kissinger. In proceedings of the 37th International Colloquium on Automata, Languages, and Programming (ICALP) 2010. Springer LNCS/ARCoSS 6199. published version | arXiv*Open Graphs and Monoidal Theories.*Lucas Dixon, Aleks Kissinger. Mathematical Structures in Computer Science, Vol 23 (Sp. Issue 2) pp. 308-359. published version | arXiv*Open Graphs and Computational Reasoning.*Lucas Dixon, Ross Duncan, and Aleks Kissinger. In proceedings of the 6th workshop on Developments in Computational Models, 2010. EPTCS 26. published version (EPTCS)*Exploring a Quantum Theory with Graph Rewriting and Computer Algebra.*In proceedings of Calculemus 2009. Springer LNCS/LNAI 5625. published version

## Talks

Below is a (partial) list of some talks I've given in the past years, along with slides.

**Quantum Circuits: From Structure to Software**. Quantum Natural Language Processing: Embracing the NISQ ERA. slides | slides (shorter) | YouTube**Picturing (and Rewriting) Quantum Processes**. 11th International School on Rewriting, Paris, 1-6 July 2019. part 1 | part 2**A categorical semantics for causal structure**. Categories Logic and Physics Scotland (CLAPS) 2017. Edinburgh. slides | YouTube**Simplification by Rotation for Frobenius/Hopf algebras**. First international workshop on string diagrams (STRING) 2017. Oxford slides**Picturing Quantum Processes**. European Summary School on Logic, Language, and Information. Toulouse 2017. slides | more slides**Algebraic (and Diagrammatic) Structures in Quantum Theory**. QuSoft Showcase, CWI Amsterdam 2016. slides**Keynote lecture: Process Theories and Graphical Language**. Biennial IQSA Conference on Quantum Structures, Leicester 2016. slides**Tutorial: Process Theories and Graphical Language**. QPL 2016. slides**Quantum teleportation, diagrams, and the one-time pad**. Radboud 2016. slides**An Introduction to Globular**. Foundational Structures in Computation and Deduction, Porto 2016. slides**Quantum Picturalism**. Quantum Foundations, London 2016. slides**Picturing Quantum Processes**. Quantum Theory, Foundations, and Technologies (QTFT). Vaxjo, Sweden 2015. slides**Picturing Quantum Entanglement in Measurement-based Quantum Computation**. Oxford 2015. slides**Diagrammatic Reasoning and Quantum Computation.**Applications of Computer Algebra (ACA), Kalamata, Greece. 2015. slides**Picturing Even More Quantum Processes**. QICS Spring School, Oxford 2014. part 2 | part 3**New reasoning techniques for monoidal algebra.**Theory Group seminar, Queen Mary 2014. slides**Interactive Proof for Diagrammatic Languages.**A Conference in Honour of Samson Abramsky, on the event of his 60th Birthday (SamsonFest). Oxford, UK 2013. slides**Pictures of non-locality in quantum mechanics.**LICS 2012. slides**The CP*-construction: A Category of Classical and Quantum Channels**. QPL, Brussels 2012. slides

*Updated 11 September, 2023.*