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Quantum Picturalism

Bob Coecke

2009 · arXiv

PhysicsMathematicsProgramming languages
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From the abstract

The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. In this review we present steps towards a diagrammatic `high-level' alternative for the Hilbert space formalism, one which appeals to our intuition. It allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the no-cloning theorem, and phenomena such as quantum teleportation. As a logic, it supports `automation'. It allows for a wider variety of underlying theories, and can be easily modified, having the potential to provide the required step-stone towards a deeper conceptual understanding of quantum theory, as well as its unification with other physical theories. Specific applications discussed here are purely diagrammatic proofs of several quantum computational schemes, as well as an analysis of the structural origin of quantum non-locality. The underlying mathematical foundation of this high-level diagrammatic formalism relies on so-called monoidal categories, a product of a fairly recent development in mathematics. These monoidal categories do not only provide a natural foundation for physical theories, but also for proof theory, logic, programming languages, biology, cooking, ... The challenge is to discover the necessary additional pieces of structure that allow us to predict genuine quantum phenomena.

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In the conversation

Original HN comments, with labels from simple text rules. A label describes the whole comment and may miss context or irony. Read the discussion to make up your own mind. About the labels

6 selected excerpts · 6 total mentions

mncharity
Neutral mention · rule
Quantum Picturalism: Learning Quantum Theory in High School https://arxiv.org/pdf/2312.03653 seems a longer version. That QPict Quantum picturalism (2009) paper is https://arxiv.org/pdf/0908.1787 . Picturing quantum processes - A first course in quantum theory and diagrammatic reasoning (2017) is https://www.cs.ox.ac.uk/people/aleks.kissinger/PQP.pdf (900+ pages; only 24 MB). Slides accessible: https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf ; slides technical: https://www.cs.ox.ac.uk/people/aleks.kissinger/slides/pdf/ak... . Quantum in Pictures (2022) does not appear to be available open access.
Original comment A particle physics course for high-school students
mathgenius
Neutral mention · rule
Apparently there is an actual experiment on six-year-olds taking place [1,2]: "Experiment. Consider ten children of ages between six and ten and consider ten high-school teachers of physics and mathematics. The high-school teachers of physics and mathematics will have all the time they require to refresh their quantum mechanics background, and also to update it with regard to recent developments in quantum information. The children on the other hand will have quantum theory explained in terms of the graphical formalism. Both teams will be given a certain set of questions, for the children formulated in diagrammatic language, and for the teachers in the usual quantum…
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mechanical formalism. Whoever solves the most problems and solves them in the fastest time wins. If the diagrammatic language is much more intuitive, it should in principle be possible for the children to win." [1] https://twitter.com/coecke/status/1285531026270367744 [2] https://arxiv.org/abs/0908.1787
Original comment Kindergarten Quantum Mechanics
mikhailfranco
Neutral mention · rule
I believe Roger Penrose draws all his own illustrations. For copius excellent examples, see his book Road to Reality. Here is one example: https://phys.org/news/2018-03-math-bridges-holography-twisto... https://theportal.wiki/images/1/11/Penrose-Rindler-Clifford-... He also comes from the pre-ppt age of presenting with handwritten acetate transparencies - and still does afaik. Many of his slides have been captured for the infowebs. http://cgpg.gravity.psu.edu/online/Html/Seminars/Fall1998/Pe... http://cgpg.gravity.psu.edu/online/Html/Seminars/Fall1998/Pe... Some of his original papers from the 1960s were not published at the time, but circulated as samizdat facsimiles of…
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his handwritten notes, until later transcribed by professors or their students, then published in book collections: http://math.ucr.edu/home/baez/penrose/Penrose-TheoryOfQuanti... Penrose is famous for his visual imagination, which seems to ground many of his insights. Here is a paper where he invents a visual notation for tensors and operators: https://en.wikipedia.org/wiki/Penrose_graphical_notation http://homepages.math.uic.edu/~kauffman/Penrose.pdf This has inspired recent work by Bob Coecke, as captured in his beautiful book Picturing Quantum Processes. (arXiv example: https://arxiv.org/pdf/0908.1787.pdf)
Original comment Have you ever asked yourself “how did research get done before LateX?”
useless
Neutral mention · rule
I think it is generally useful for people to have a picture in their head about whats going on as work quite frequently gets lead by instinct and educated guesswork which can be made rigorous once you've decided its worth the time to do so. That said I really don't understand the appeal of Bohmian mechanics. The explicit non-locality puts me off it. On a more positive note the stuff about category theory is very interesting and I think has a lot to offer physics in general and quantum mechanics in particular. I found a couple of papers by Bob Coecke made a good introduction to the use of categories for a physicist: 1) http://arxiv.org/abs/0908.1787 2) http://arxiv.org/abs/0808.1032
Original comment The Wholeness of Quantum Reality: An Interview with Physicist Basil Hiley
mncharity
Neutral mention · rule
From [0] 2018: "In [1] we present an entirely diagrammatic presentation of quantum the-ory with applications in quantum foundations and quantum information.This was the result of many years of work by many, and started of as acategory-theoretic axiomatisation motivated by computer science as well asaxiomatic physics. However, I have always felt that the diagrammatic pre-sentation is of great use in its own right, be it to bridge disciplines, makequantum theory more easy to grasp, or, for educational purposes, in [2] wemade the bolt claim that using diagrams high-school kids could even out-perform their teachers, or university students. Now, we will put this claimto the…
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test. To do so, we have written two tutorials [3,4], covering exactlythe same material, but one only using diagrams, while the other containsthe standard Hilbert space presentation. There are corresponding sets ofexamples too." [0] Quantum Theory for Kids https://repositorio.usp.br/directbitstream/95d90813-2c2f-4cc... [1] Picturing Quantum Processes https://doi.org/10.1017/9781316219317 ; slides https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf ; talk https://www.youtube.com/watch?v=7Fvjpjhimic [2] Quantum Picturalism https://arxiv.org/abs/0908.1787 [3] Quantum theory in Pictures ... "Top Secret"... I didn't quickly find. A recent talk: https://www.youtube.com/watch?v=AOLoyx6EHq8
Original comment Kindergarten Quantum Mechanics
mathgenius
Neutral mention · rule
Quantum computing is all about the tensor product. This is, roughly, how "and" works in the quantum world. Learning about tensor products by calculating with matrices is dizzyingly complicated [1]. But there's another way, using string diagrams [2]. [1] https://en.wikipedia.org/wiki/Kronecker_product [2] https://arxiv.org/abs/0908.1787
Original comment A brief introduction to quantum computing

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