harnywang

Representing everything in string diagrams, with rewriting as computation, inspired by the Yogacara School.

[harnywang @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. https://t.co/xgcpP7YYTR

[harnywang @harnywang]

@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.

[Quantum @quantumjournal]

Fresh in Quantum: Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning by Quanlong Wang, Richie Yeung, and Mark Koch https://t.co/STrpeguF8C

[harnywang @harnywang]

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

[harnywang @harnywang]

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. https://t.co/zZ9OKa9WIQ

[harnywang @harnywang]

@thomasahle Maybe even the same. We have a normal form diagram for any tensor as shown in this paper: https://t.co/EuNQrtj82x

[harnywang @harnywang]

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

[Department of Physics at University of Oxford @OxfordPhysics]

Poster making at Oxford Earth Day 2024. Doors are open until 4pm today. See event page for more information: https://t.co/JypaNOJgEo

[harnywang @harnywang]

@AlexisToumi Very well summarised, many thanks!

[harnywang @harnywang]

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:https://t.co/DuEy5yw4Ak

[harnywang @harnywang]

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

[harnywang @harnywang]

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

[harnywang @harnywang]

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!

[harnywang @harnywang]

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

[harnywang @harnywang]

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!

[Quantinuum @QuantinuumQC]

Quantinuum researchers are developing a unique approach to mathematics, promising new solutions to old problems.

Read more here: https://t.co/HOqizsFABe

[harnywang @harnywang]

@cole_comfort Congrats!

[harnywang @harnywang]

@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.

[harnywang @harnywang]

@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.

[harnywang @harnywang]

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.
https://t.co/EuNQrtj82x