harnywang

Two years ago we started a discussion in a pub on the irreducible representation of SU(2) in a compact form of ZX diagrams. Now it becomes a paper on arXiv, with multiple applications including quantum computing and loop quantum gravity. arxiv.org/abs/2511.06012

@thomasahle @quantumjournal @TomHardyofmath The goal is to get a single diagram instead of a sum of diagrams after taking the derivative, though we already used the product rule to obtain the differentiated diagram.

@quantumjournal @TomHardyofmath Can't you just take the derivative using the product rule, like with normal tensor diagrams? en.m.wikipedia.org/wiki/Penrose_g…

Fresh in Quantum: Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning by Quanlong Wang, Richie Yeung, and Mark Koch doi.org/10.22331/q-202…

I just proved the following Fundamental Binor Identity in the ZXW calculus, it is fun!

We just updated our paper on differentiating and integrating ZX diagrams. Now there’s no need of distinguishing different cases for the general differentiation theorem, and the integration diagram works for arbitrary number of pairs of phases. arxiv.org/abs/2201.13250…

@thomasahle Maybe even the same. We have a normal form diagram for any tensor as shown in this paper: arxiv.org/abs/2309.13014

@harnywang Right, I think tensor diagrams are quite similar to string diagrams. en.m.wikipedia.org/wiki/Penrose_g…

KANs (NNs with learned functions on the edges) have a quite elegant representation using Tensor Diagrams. This chart of MLP layers also shows some neat relationship between things like ReGLUs and MoEs.

Thanks for organising the event, the first one is from my daughter 😀

@AlexisToumi Very well summarised, many thanks!

The end of (the beginning of) a 15 year journey into formalising finite dimensional vector spaces and tensor product purely in terms of diagrams, snakes, spiders, cups and caps 🐍🕷️☕️🧢

Finite dimensional quantum theory has a complete graphical language now! Also the Z spider could have legs with different dimensions, which is key for our way of constructing spin networks. Check out the newly added application section for more details:arxiv.org/abs/2309.13014…

@marstonbikepath The cycle path closed this morning, does anyone know how it is now?

@SubhayanRM Cool, I happen to know how to depict any SU(n) irreps in qufinite ZX-calculus 😁

quantum Algs can be represented with SU(N), i.e., compact Lie group, and can be endowed with a metric structure associated with computational complexity. The optimal circuit, V, may be then associated to a shortest geodesic between id & V. Clever, right? arxiv.org/abs/quant-ph/0…

Can you believe it, I just calculated the following Wigner’s 3j-symbol by qufinite ZX-calculus using rewriting skills and got exactly the same result!

@JohannesKleiner @Robert_Prentner Congratulations @Robert_Prentner. Can you believe I have never been to Shanghai before?

The first professorship for #Mathematical #Consciousness #Science dropped! Super huge congratulations to @Robert_Prentner 🎉🎉🎉 Very glad you made it, Robert, and also that MCS will have a future in Shanghai!

With this work coming out, I am finally released from doing any more on completeness. Excitingly, we have recently found applications of this framework to graphically rewriting for spin networks, please stay tuned for our next paper!

@cole_comfort Congrats!

@cole_comfort If we use the X spiders (as defined in the paper) instead of qudit Hadamard as generators, then the completeness result can be generalised to (Mat(R),\otimes) for any commutative semiring R.

@cole_comfort At the beginning we thought we may need some factorisation into power of primes for the completeness proof, but fortunately we found that’s not necessary.

We put all the qudit ZXW calculi in a single framework and made it complete, now any equality of tensors can be derived purely diagrammatically. Also the unified framework is equivalent to FdHilb, so feel free to construct your quantum theory with it. arxiv.org/abs/2309.13014