Kindergarten Quantum Mechanics, now for real!

Abstract: Over some 20 years we have developed a diagrammatic quantum formalism, sometimes referred to as quantum picturalism, or categorical quantum mechanics. We have written two books on it [2, 3]. This project was in part initiated in a talk some 20 years ago, with the title Kindergarten Quantum Mechanics [1]. Two things have happened since:

(1) We showed that this formalism enabled secondary school students to perform exceptionally well on an Oxford University post-grad quantum exam, as reported in The Guardian/Observer [4]. Almost 50% of the students obtained a distinction, and 80% passed [5]. Those numbers are better than typical Oxford University MSc students. In Greece quantum picturalism is already used to teach quantum at secondary school level, and several other countries are in the process of doing so too.

(2) John von Neumann himself who denounced `his own’ quantum formalism, that relies on Hilbert space. Alternatives had been proposed, including by von Neumann himself, but none play a role in quantum theory today. On the other hand, quantum picturalism is now widespread in quantum industry, with applications including circuit optimisation and error-correction, with Peter Shor among the proponents. The formalism is also used as the basis for interpretable AI, and even music [6].

Hence quantum picturalism has succeeded in providing an alternative formalism for quantum, with several advantages over the usual formalism, be it as an educational tool, an engineering tool, or a vehicle to explore applications in new areas.

[1] Bob Coecke (2006) Kindergarten quantum mechanics. Quantum Theory: Reconstructions of the Foundations III. AIP Conference Proceedings. Vol. 810. No. 1. American Institute of Physics.

[2] Bob Coecke & Aleks Kissinger (2017) Picturing Quantum Processes. Cambridge University Press.

[3] Bob Coecke & Stefano Gogioso (2022) Quantum in Pictures. Quantinuum.

[4]https://www.theguardian.com/science/2023/dec/16/physicist-bob-coecke-its-easier-to-convince-kids-than-adults-about-quantum-mechanics

[5] Selma Dündar-Coecke, Caterina Puca, Lia Yeh, Hamza Waseem, Emmanuel Pothos, Thomas Cervoni, Sieglinde M-L. Pfaendler, Vincent Wang-Maścianica, Peter Sigrist, Ferdi Tomassini, Vincent Anandraj, Ilyas Khan, Stefano Gogioso, Aleks Kissinger, & Bob Coecke (2025). Making the quantum world accessible to young learners through Quantum Picturalism: An experimental study. arXiv preprint arXiv:2504.01013.

[6] www.youtube.com/watch?v=-7q7n8TYPdo

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Speaker Bio: Professor Coecke is a theoretical physicist and logician, and a former Chief Scientist at Quantinuum, leading its Quantum-Compositional Intelligence (QCI) research team. He is also Distinguished Visiting Research Chair at Perimeter Institute for Theoretical Physics, Emeritus Professor at Wolfson College, Oxford University, and a Visiting Fellow at the Computer Science Department and the Mathematical Institute of Oxford University.

He is a founding father of the QPL (Quantum Physics and Logic) and ACT (Applied Category Theory) communities, of the diamond-open-access journal Compositionality, and Cambridge University Press' Applied Category Theory book series.

He is best known for pioneering a simple, picture-based approach to quantum mechanics—sometimes called “Kindergarten Quantum Mechanics”—that allows anyone to grasp quantum ideas with no formal background in mathematics.

www.cs.ox.ac.uk/people/bob.coecke/

Bob Coecke

Wolfson College Oxford, Perimeter Institute

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Moderator: The talk will be moderated by Priyaa Varshinee Srinivasan. Priyaa is a postdoctoral fellow at the Tallinn University of Technology researching categorical quantum mechanics. Her vision is for everyone to experience the joy of mathematics in their own way. She has co-authored a live digital book titled “Relational thinking: from abstractions to applications” which reveals the thought-process behind creating mathematics (category theory) using story-telling, illustrations, and visualization of computations. The material is available at toposinstitute.github.io/RelationalThinking-Book/cover.html.

Computer scienceMathematics

Audience: researchers in the topic

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Relatorium seminar

Series comments: The name "Relatorium" combines "relator" with the Latin root "-ium," meaning "a place for activities" (as in "auditorium" or "gymnasium"). This seminar series is a platform to relate ideas, interact with math, and connect with each other.

In this series, we explore math beyond what we usually hear in standard talks. These sessions fall somewhere between a technical talk and a podcast: moderately formal, yet conversational. The philosophy behind the series is that math is best learned by active participation rather than passive listening. Our aim is to “engage and involve,” inviting everyone to think actively with the speaker. The concepts are accessible, exploratory, and intended to spark questions and discussions.

The idea of relatability has strong ties to compassion — creating space for shared understanding and exploration - which is the spirit of this seminar! This is a pilot project, so we’re here to improvise, learn, and evolve as we go!

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