Fawly

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Happy editing! ~Oshwah~^{(talk) (contribs)} 07:55, 7 December 2020 (UTC)

Quantum computing reference

Hi, I put a question on the talk page about your citation for quantum computing. The Scientific American article includes hybrid computers. That is like saying "A petrol car can have as low a carbon footprint as an electric car" and including a reference to an article about HYBRID cars which says, you can turn off the petrol engine completely.Createangelos (talk) 10:47, 7 December 2020 (UTC)

Hi! I responded on the talk page, but also I think you might be looking at the wrong reference? I cited reference 12, not 11. Fawly (talk)

Yes, I see I clicked the link on the Scientific American article rather than the textbook. I've found it and am having a look now...Createangelos (talk) 16:48, 7 December 2020 (UTC)

I see what you're saying about 'abstract' as the Nielsen def'n does indeed seem (too?) abstract. It is trivial to simulate boolean logic reversibly...Createangelos (talk) 16:53, 7 December 2020 (UTC)

Yeah, the definition used is the quantum analogue to the Turing machine, which is typical in the computability world where one asks questions like "Can computational models X and Y solve the same problems?". Another way to think about this is that the quantum logic gates that universal quantum computers wish to implement always includes a universal gate set for reversible computing. So, in a world with perfect qubits, the quantum computers we have now would be able to perform (small) reversible boolean logic computations. Quantum computers generalize classical computers, so the statement I was trying to make is a trivial one. Hope this helps. Fawly (talk)

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Solovay-Kitaev theorem

Hello Fawly. I see that you have worked on the page for the Solovay-Kitaev theorem, and I wanted to mention that I recently improved the polylog exponent in the theorem from $c=3+\delta$ to $c=\log _{\phi }2+\delta =1.44042\ldots +\delta$. My paper on this is arXiv:2306.13158; it has been submitted for publication, but it is already peer-reviewed in the sense that I presented at QIP 2023. I am mentioning this to you because: (a) Many people in QC have only a cursory understanding of the Solovay-Kitaev topic, and the Wikipedia page is pretty good and Wikipedia is generally influential. Also (b) I don't want to make any edits myself in Wikipedia that could be taken as self-promotion. Greg Kuperberg (talk) 18:40, 10 January 2024 (UTC)

Of course! Definitely think your work belongs in the page; made the relevant edits. Fawly (talk) 22:30, 11 January 2024 (UTC)

Great, thanks a lot! I would only suggest either adding "where $\phi$ is the golden ratio" in the sentence you added, or replacing the formula $\log _{\phi }2$ by $\log _{(1+{\sqrt {5}})/2}2$. Greg Kuperberg (talk) 03:48, 13 January 2024 (UTC)

Oh actually I just noticed another issue with the page, that maybe I can fix but for now I'll just put in your corner. Your citation for the $c=1$ result (Harrow, Recht, and Chuang) is one that shows existence of short words but no efficient algorithm to find them, for special gate sets. However, you can also get existence and an efficient algorithm for special gate sets, in particular for the widely used Clifford+T gate set. The best citation for this is Ross and Selinger, arXiv:1403.2975. Greg Kuperberg (talk) 03:53, 13 January 2024 (UTC)

I went ahead and made some changes myself to the page Solovay–Kitaev theorem. Greg Kuperberg (talk) 18:20, 16 January 2024 (UTC)