ZX calculus is very interesting framework for doing cutting edge research in error correction and gate compilation, but it seems wildly off base as a means of making quantum computing accessible to a broader audience. Anything beyond the simple "teleportation is like pulling a string" picture is extremely difficult abstract manipulations.
(PhD in experimental QC)
For those of us who have decent computer science and math education and are curious about QC but have jobs in classical computing, are there any resources you recommend that are a better introduction? I understand something about being able to test large numbers of permutations of something at once, or square rooting the number of necessary operations for some functions...
My understanding is ZX calculus is more like a “calculus” or a nice toolkit. So you probably still cannot bypass regular QC formalism (being able to manipulate things fast doesn’t mean you necessarily understand it well)
>High-schoolers excelling at Oxford Uni post-grad quantum exam, thanks to Quantum Picturalism!
thoughts?
They didn't give the stdents the full post-grad exam. They cherry picked a few of the questions that can be solved with this method. It's handy for a few special cases, but not in general.
I somewhat agree. I think the goal would be to create a UI that allows you to do the ZX calculus by just creating/moving/joining the spiders etc.
IANAP so got curious about how ZX Calculus related to Feynman Diagrams (if at all)
Search landed on this neat summary [^1] (2024) from the lab(?) which also has a link to the original paper [^2]
Both are diagrammatic but that's all the overlap there is.
Feynman diagrams are a way to compute Green's functions/propagators for particle scattering amplitudes. IOW they give a pictorial representation of things you need to compute to figure out particle reactions at high energies.
ZX calculus is for "simplifying" quantum circuits. I write this in quotes because the rules are pretty involved. Apart from Quantinuum, few (if any) are pushing for it. Almost no quantum computing papers are published using ZX notation.
Feynman diagrams in particle physics are, however, universal.
Sadly, the only way to truly “understand” quantum physics is through math. A “shut up and calculate” approach.
Now, my rant.
The main reason math often seems more complicated than it really is has to do with the use of strange symbols and naming conventions. It also feels like academia in the US intentionally uses non-plain language and terminology to sound smarter and exclusive.
Back in socialist countries, there was a strong effort to name these concepts using “normal” language, and that really helped. When I came to US, I’d see something like Fourier transformation and think, “Why do use this strange name?” Why not call it “conversion of a signal into frequencies” (lose translation).
Of course, maybe the reason is that it is easier to create a new word/term in Slavic languages.
Their pictoral representation is a "shut up and calculate" notation, you can always map it 1:1 with the linear algebra formulation. It was developed as a better tool of thought for working out proofs in QC.
I had the pleasure of interacting with Duncan and Bob when XZ calculus was being developed. While I did not use their calculus for my own research, it did inspire the graphical notation I doodled with.
While I agree that naming a thing after a person makes it less clear at first glance, it is definitely not to intentionally sound smarter and exclusive; it's simply a handy short label for often subtle and complex things in an environment where you are constantly referring to it. New fields or domains will typically develop their own notation, as they often require new tools of thought. I'm sure you are not suggesting that Feynman diagrams or Einstein summations making things more complicated than they really are.
To your point: the annoying part is when the conventions clash. In early QC works an X could be the X-gate or something else completely. A good chunk of the effort in writing or understanding a QC publication was establishing the notation. After a while notation gets a bit more consolidated as conventions get naturally established. Of course, if you move from a world that has established its own conventions, e.g. behind the iron curtain, it can be frustrating to be confronted with the many eponyms in a field where you already have deep expertise. I had similar experiences just from working in teams that were using different programming languages: "Why call it a SAX parser? That's just tree-recursive descent!"
As if that is the problem with mathematics. 99.9% of mathematics isn't about how things are named. There are zero persons in the world who failed to understand the Fourier transform because of its name.
I think you are maybe right here.
Math needs to be this way for precision. There are dozens of "conversions of signal into frequencies" besides Fourier transform: Z-transform, Laplace tansform, Wigner transform and so on. Normal language deals with few concepts, math deals with thousands.
Soviet countries wanted to isolate their peoples from western ideas. If you start teaching about Fourier transform in schools, students are going to ask who that Fourier is.
Can you give a less trivial example? How would different wording help with understanding the proof of Greene's theorem, for example? When it comes down to it, it's just complicated stuff.
Maybe seeing strange symbols appears like gatekeeping to you, but surely we agree that there is also a more amicable explanation: symbols are quick to write, which makes it easier to manipulate equations with pen and paper or on a blackboard, and eventually you run out of symbols and have to resort to more exotic ones. Obviously it's up to you which explanation you prefer, but in my view you should have stronger evidence if you imply malicious intent or properties like arrogance.
The jumble of letters Fourier says nothing about what a Fourier Transform is or does. Signalidominomorphosis, or just dominomorphosis, tells a lot more at face value than Fourier Transformation which just basically says "a transformation associated with a Fourier."
With the loss of the old liberal education, we are forgetting our words are like pictograms, compiled from meaningful components from the shoulders of classical languages and ideas. Etymology books should be as common as dictionaries!
(don't mind me, just trying to anonymously add to the dictionary)
One thing that mathematicians do quite commonly is look at the same object in several different ways. The "Fourier Transform" is "Signalidominomorphosis" but it is also a linear operator on the vector space of functions, and something more complicated from the perspective of measure theory. For theoretical physicists, it plays yet a different role when applied to wave functions.
The disadvantage of naming a thing using one of the things it does, is that it focuses you too much on that one use case. Giving arbitrary names actually frees you to think of the object in whatever way is useful for the problem at hand.
I don't see how your reply is related to my post, but anyway.
> The jumble of letters Fourier says nothing about what a Fourier Transform is or does. Signalidominomorphosis, or just dominomorphosis, tells a lot more at face value than Fourier Transformation which just basically says "a transformation associated with a Fourier."
On the contrary. The jumble of letters tells you precisely what a Fourier transform is or does after you learn what the letters mean.
Telling someone "Signalidominomorphosis" does not enable them to find the Fourier transform of the double-sided exponential.
>Why not call it “conversion of a signal into frequencies”
I agree, there has to be a combination of Greek & Latin parts to compile into a Germanic-style adjective sandwich of a word which describes the Fourier.
Interpolation is one such word:
Inter - between/among,
pol - fill/smooth/polish,
ation - action or process of the foregoing.
May I propose 'Signalidominotransform' or 'Signalidominomorphosis' as candidates to replace "Fourier Transformation?"
I don’t understand this name. I see “signal” (which seems more related to an application of Fourier transforms?) and “domino”? I don’t get the “domino” part.
In any case, it is way longer.
[deleted]
> it is easier to create a new word/term in Slavic languages.
Why is this the case?
> The term, “Quantum Picturalism” was coined to describe this unique approach of teaching quantum concepts visually, reducing intimidation and opening the field to broader audiences.
ZX calculus is very interesting framework for doing cutting edge research in error correction and gate compilation, but it seems wildly off base as a means of making quantum computing accessible to a broader audience. Anything beyond the simple "teleportation is like pulling a string" picture is extremely difficult abstract manipulations.
(PhD in experimental QC)
For those of us who have decent computer science and math education and are curious about QC but have jobs in classical computing, are there any resources you recommend that are a better introduction? I understand something about being able to test large numbers of permutations of something at once, or square rooting the number of necessary operations for some functions...
edit: found this below, but it is all ZX calculus
https://zxcalc.github.io/book/html/main_html.html
My understanding is ZX calculus is more like a “calculus” or a nice toolkit. So you probably still cannot bypass regular QC formalism (being able to manipulate things fast doesn’t mean you necessarily understand it well)
https://x.com/coecke/status/1907809898852667702
>High-schoolers excelling at Oxford Uni post-grad quantum exam, thanks to Quantum Picturalism!
thoughts?
They didn't give the stdents the full post-grad exam. They cherry picked a few of the questions that can be solved with this method. It's handy for a few special cases, but not in general.
I somewhat agree. I think the goal would be to create a UI that allows you to do the ZX calculus by just creating/moving/joining the spiders etc.
IANAP so got curious about how ZX Calculus related to Feynman Diagrams (if at all)
Search landed on this neat summary [^1] (2024) from the lab(?) which also has a link to the original paper [^2]
[1]: https://www.quantinuum.com/blog/quantinuum-scientists-have-p...
[2]: https://arxiv.org/abs/2405.10896
Just to add, buried away there is this gh repo also: https://github.com/zxcalc/book
Ooh thanks, totally missed this!
Both are diagrammatic but that's all the overlap there is.
Feynman diagrams are a way to compute Green's functions/propagators for particle scattering amplitudes. IOW they give a pictorial representation of things you need to compute to figure out particle reactions at high energies.
ZX calculus is for "simplifying" quantum circuits. I write this in quotes because the rules are pretty involved. Apart from Quantinuum, few (if any) are pushing for it. Almost no quantum computing papers are published using ZX notation.
Feynman diagrams in particle physics are, however, universal.
You might enjoy this write-up: https://pennylane.ai/qml/demos/tutorial_zx_calculus
Sadly, the only way to truly “understand” quantum physics is through math. A “shut up and calculate” approach.
Now, my rant.
The main reason math often seems more complicated than it really is has to do with the use of strange symbols and naming conventions. It also feels like academia in the US intentionally uses non-plain language and terminology to sound smarter and exclusive.
Back in socialist countries, there was a strong effort to name these concepts using “normal” language, and that really helped. When I came to US, I’d see something like Fourier transformation and think, “Why do use this strange name?” Why not call it “conversion of a signal into frequencies” (lose translation).
Of course, maybe the reason is that it is easier to create a new word/term in Slavic languages.
Their pictoral representation is a "shut up and calculate" notation, you can always map it 1:1 with the linear algebra formulation. It was developed as a better tool of thought for working out proofs in QC.
I had the pleasure of interacting with Duncan and Bob when XZ calculus was being developed. While I did not use their calculus for my own research, it did inspire the graphical notation I doodled with.
While I agree that naming a thing after a person makes it less clear at first glance, it is definitely not to intentionally sound smarter and exclusive; it's simply a handy short label for often subtle and complex things in an environment where you are constantly referring to it. New fields or domains will typically develop their own notation, as they often require new tools of thought. I'm sure you are not suggesting that Feynman diagrams or Einstein summations making things more complicated than they really are.
To your point: the annoying part is when the conventions clash. In early QC works an X could be the X-gate or something else completely. A good chunk of the effort in writing or understanding a QC publication was establishing the notation. After a while notation gets a bit more consolidated as conventions get naturally established. Of course, if you move from a world that has established its own conventions, e.g. behind the iron curtain, it can be frustrating to be confronted with the many eponyms in a field where you already have deep expertise. I had similar experiences just from working in teams that were using different programming languages: "Why call it a SAX parser? That's just tree-recursive descent!"
As if that is the problem with mathematics. 99.9% of mathematics isn't about how things are named. There are zero persons in the world who failed to understand the Fourier transform because of its name.
I think you are maybe right here.
Math needs to be this way for precision. There are dozens of "conversions of signal into frequencies" besides Fourier transform: Z-transform, Laplace tansform, Wigner transform and so on. Normal language deals with few concepts, math deals with thousands.
Soviet countries wanted to isolate their peoples from western ideas. If you start teaching about Fourier transform in schools, students are going to ask who that Fourier is.
Can you give a less trivial example? How would different wording help with understanding the proof of Greene's theorem, for example? When it comes down to it, it's just complicated stuff.
Maybe seeing strange symbols appears like gatekeeping to you, but surely we agree that there is also a more amicable explanation: symbols are quick to write, which makes it easier to manipulate equations with pen and paper or on a blackboard, and eventually you run out of symbols and have to resort to more exotic ones. Obviously it's up to you which explanation you prefer, but in my view you should have stronger evidence if you imply malicious intent or properties like arrogance.
The jumble of letters Fourier says nothing about what a Fourier Transform is or does. Signalidominomorphosis, or just dominomorphosis, tells a lot more at face value than Fourier Transformation which just basically says "a transformation associated with a Fourier."
With the loss of the old liberal education, we are forgetting our words are like pictograms, compiled from meaningful components from the shoulders of classical languages and ideas. Etymology books should be as common as dictionaries!
(don't mind me, just trying to anonymously add to the dictionary)
One thing that mathematicians do quite commonly is look at the same object in several different ways. The "Fourier Transform" is "Signalidominomorphosis" but it is also a linear operator on the vector space of functions, and something more complicated from the perspective of measure theory. For theoretical physicists, it plays yet a different role when applied to wave functions.
The disadvantage of naming a thing using one of the things it does, is that it focuses you too much on that one use case. Giving arbitrary names actually frees you to think of the object in whatever way is useful for the problem at hand.
I don't see how your reply is related to my post, but anyway.
> The jumble of letters Fourier says nothing about what a Fourier Transform is or does. Signalidominomorphosis, or just dominomorphosis, tells a lot more at face value than Fourier Transformation which just basically says "a transformation associated with a Fourier."
On the contrary. The jumble of letters tells you precisely what a Fourier transform is or does after you learn what the letters mean.
Telling someone "Signalidominomorphosis" does not enable them to find the Fourier transform of the double-sided exponential.
>Why not call it “conversion of a signal into frequencies”
I agree, there has to be a combination of Greek & Latin parts to compile into a Germanic-style adjective sandwich of a word which describes the Fourier.
Interpolation is one such word:
Inter - between/among,
pol - fill/smooth/polish,
ation - action or process of the foregoing.
May I propose 'Signalidominotransform' or 'Signalidominomorphosis' as candidates to replace "Fourier Transformation?"
I don’t understand this name. I see “signal” (which seems more related to an application of Fourier transforms?) and “domino”? I don’t get the “domino” part.
In any case, it is way longer.
> it is easier to create a new word/term in Slavic languages.
Why is this the case?
> The term, “Quantum Picturalism” was coined to describe this unique approach of teaching quantum concepts visually, reducing intimidation and opening the field to broader audiences.