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[QUOTE=rogue;527615][URL="https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-to-multiply-20190411/"]Mathematicians Discover the Perfect Way to Multiply[/URL]
<snip>[/QUOTE]
One of the authors, David Harvey, has a link in his publications list about the paper, [url=https://web.maths.unsw.edu.au/~davidharvey/papers/nlogn/][i]Integer multiplication in time O(n log n)[/i][/url]. The page has a FAQ and a link to a preprint.

[QUOTE=Dr Sardonicus;527676]One of the authors, David Harvey, has a link in his publications list about the paper, [url=https://web.maths.unsw.edu.au/~davidharvey/papers/nlogn/][i]Integer multiplication in time O(n log n)[/i][/url]. The page has a FAQ and a link to a preprint.[/QUOTE]

Note that the Quanta paper is dated 11 April 2019 - it and the preprints it was based on were linked/discussed both [url=https://www.mersenneforum.org/showthread.php?p=512741#post512741]in this very same thread[/url] and in [url=https://mersenneforum.org/showthread.php?t=19486]this one[/url] in the Computer Science & Computational Number Theory subforum. Also, David Harvey's page has a truly LOL-worthy snip of the kind only a mathematician could make with a straight face:
[quote] Much internet commentary has focused on the quantity n[sub]0[/sub] = 2[sup]1729^12[/sup] appearing in the paper. This number is roughly 10[sup]214857091104455251940635045059417341952[/sup].

Some people have asserted that the new algorithm only works for n ≥ n[sub]0[/sub], and/or that the algorithm only becomes faster than previous algorithms for n ≥ n[sub]0[/sub]. These assertions are somewhat misleading.

For n < n[sub]0[/sub], the new algorithm is [i]by definition[/i] no faster than existing algorithms, because it calls an existing algorithm to do its work. The value n[sub]0[/sub] is simply an explicit threshold that was chosen to ensure that the inductive step of our proof of the complexity bound works out correctly. The actual value was chosen to make the proof as straightforward as possible; it was not chosen to optimise the overall running time.

On the other hand, for n slightly larger than n[sub]0[/sub], the new algorithm might turn out to be either faster or slower than existing algorithms. This depends on, among other things, the implied big-O constants for both the new algorithm and the algorithm with which it is being compared. Since we do not know (yet) what these constants are, we cannot tell which is faster. [/quote]
Hmm, "for n slightly larger than n0" - wonder what he means by 'slightly' - n ≥ n[sub]0[/sub][sup]2[/sup],perhaps? Or maybe n ≥ 2^n[sub]0[/sub]? Inquiring minds at the GIMPS wavefront want to know!

Upshot: The result is of great theoretical interest - even moreso would be proving whether or not O(n log n) is in fact a lower bound on multiplicational complexity - but of little or no practical utility.

[QUOTE=ewmayer;527689]Note that the Quanta paper is dated 11 April 2019 - it and the preprints it was based on were linked/discussed both [url=https://www.mersenneforum.org/showthread.php?p=512741#post512741]in this very same thread[/url] and in [url=https://mersenneforum.org/showthread.php?t=19486]this one[/url] in the Computer Science & Computational Number Theory subforum.[/QUOTE]
Ahh. Thank you. I [i]knew[/i] I'd seen [i]something[/i] about the computational difficulty of multiplication -- [i]somewhere[/i] -- not that long ago, but couldn't remember where or when. [i]That's it![/i]

Of course, it didn't occur to me to search the Forum. I went straight for a primary source.
:missingteeth:

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There's a lot of chatter about Google's claim of "quantum supremacy." The Google AI Blog post [url=https://ai.googleblog.com/2019/10/quantum-supremacy-using-programmable.html]Quantum Supremacy Using a Programmable Superconducting Processor[/url] uses the phrase 11 times, and describes what they did as follows:[quote]The Experiment
To get a sense of how this benchmark works, imagine enthusiastic quantum computing neophytes visiting our lab in order to run a quantum algorithm on our new processor. They can compose algorithms from a small dictionary of elementary gate operations. Since each gate has a probability of error, our guests would want to limit themselves to a modest sequence with about a thousand total gates. Assuming these programmers have no prior experience, they might create what essentially looks like a random sequence of gates, which one could think of as the "hello world" program for a quantum computer. Because there is no structure in random circuits that classical algorithms can exploit, emulating such quantum circuits typically takes an enormous amount of classical supercomputer effort.

Each run of a random quantum circuit on a quantum computer produces a bitstring, for example 0000101. Owing to quantum interference, some bitstrings are much more likely to occur than others when we repeat the experiment many times. However, finding the most likely bitstrings for a random quantum circuit on a classical computer becomes exponentially more difficult as the number of qubits (width) and number of gate cycles (depth) grow.[/quote]So, the task seems to be "finding the most likely bitstring for a random quantum circuit."

I'm no computer expert, but it seems to me that defining the [i]task[/i] in terms of quantum circuitry gives quantum computing an unfair advantage.

They describe their "Sycamore" processor as (besides being superconducting in the title), [quote]We developed a new 54-qubit processor, named “Sycamore”, that is comprised of fast, high-fidelity quantum logic gates, in order to perform the benchmark testing.[/quote]

An article with the same title as the blog post is, it says, published in [url=https://nature.com/articles/s41586-019-1666-5]NATURE[/url].

Indeed, Google's problem definition does seem rather self-referential ... presumably if they really have the goods we can look forward to something of genuine interest, such as a quantum factoring result of a nontrivial integer, in the not-too-distant future. Here another article on the claim, which focuses with IBM's truly inane objection to the Google claim:

[url=https://www.quantamagazine.org/google-and-ibm-clash-over-quantum-supremacy-claim-20191023/]Google and IBM Clash Over Milestone Quantum Computing Experiment[/url] | Quanta Magazine

--------------------------

And on a quite different note - this seems like something a bee-friendly DIYer could do an a suitable backyard tree:

[url=https://www.reuters.com/article/us-california-beekeeper/rewilding-one-california-mans-mission-to-save-honey-bees-idUSKBN1X31CE]'Rewilding:' One California man's mission to save honey bees[/url] | Reuters

[QUOTE=ewmayer;528830]<snip>
And on a quite different note - this seems like something a bee-friendly DIYer could do an a suitable backyard tree:

[url=https://www.reuters.com/article/us-california-beekeeper/rewilding-one-california-mans-mission-to-save-honey-bees-idUSKBN1X31CE]'Rewilding:' One California man's mission to save honey bees[/url] | Reuters[/QUOTE]There's another tree thing thing that can sometimes be done. This applies to private and municipal trees alike.

If a bee tree -- a hollow tree with a beehive in it -- becomes a hazard (in danger of falling down), it has to be removed. If it's not an emergency removal, there might be time to summon a beekeeper and get the bees relocated. That would save a colony.

If a lot of people adopt the practice of "rewilding" bees near agricultural areas whose crops depend on bee pollination, I suppose it is possible that commercial beekeepers who cart their bees around to pollinate crops might object.

I mention this because some years back, I talked to the owner of a local commercial apiary about the decline of honeybees. He was aware of the problems with multiple mite infestations and insecticides, but told me that he hadn't had any major problems. He said he thought the stress on agricultural pollination bees due to their being trucked around was a major factor in colonies dying off. Without that added stress, "stay-at-home" colonies are more likely to survive the hazards they encounter.

o [url=https://www.gizmodo.com.au/2019/10/modern-humans-inherited-even-more-dna-from-neanderthals-and-denisovans-than-we-thought/]Modern Humans Inherited Even More DNA From Neanderthals And Denisovans Than We Thought[/url] | Gizmodo Australia

o [url=https://www.sciencemag.org/news/2019/10/new-universe-miniproteins-upending-cell-biology-and-genetics]New universe of miniproteins is upending cell biology and genetics[/url] | Science
[quote]How important small proteins will be for medicine is still unknown, but they have already upended several biological assumptions. Geneticist Norbert Hübner of the Max Delbrück Center for Molecular Medicine in Berlin and colleagues found dozens of new microproteins in human heart cells. The group traced them to an unexpected source: short sequences within long noncoding RNAs, a variety that was thought not to produce proteins. After identifying 169 long noncoding RNAs that were probably being read by ribosomes, Hübner and his team used a type of mass spectrometry to confirm that more than half of them yielded microproteins in heart cells, a result reported earlier this year in Cell.[/quote]

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