Talk:Quantum algorithm: Difference between revisions

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== Merging with the Quantum Algorithm Zoo? ==

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== "Exponential speedup" ==

It is extremely common to use "exponential speedup" very loosely, and say that Shor's algorithm provides an exponential speedup over GNFS. However, given that GNFS already provides sub-exponential factoring (that is, faster than $$<math>c^n$$</math> for any $$<math>c > 0$$</math>), we should probably change the last sentence in the leading paragraph which claims that Shor's algorithm provides an "exponential speedup". Thoughts?

: I changed the lede to say "much (almost exponentially) faster" rather than "exponentially faster". [[User:Sanpitch|Sanpitch]] ([[User talk:Sanpitch|talk]]) 20:31, 19 March 2019 (UTC)

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What does that even mean? Surely it doesn't want to imply Grover's algorithm runs in <math>O \left(\frac{1}{N}\right)</math>, making it faster the more there is to search in.

[[Special:Contributions/62.216.5.216|62.216.5.216]] ([[User talk:62.216.5.216|talk]]) 15:28, 21 April 2021 (UTC)

== Quanta Magazine article ==

I just saw this: https://www.quantamagazine.org/quantum-algorithms-conquer-a-new-kind-of-problem-20220711/ [[User:Billymac00|Billymac00]] ([[User talk:Billymac00|talk]]) 21:51, 14 July 2022 (UTC)

== The use of the adverb "probably" ==

There are numerous cases of the use of the adverb "probably" in the article that are imprecise, inappropriate, and take away from the professionalism and encyclopediac tone of the article. I'd consider removing them. [[Special:Contributions/205.189.94.9|205.189.94.9]] ([[User talk:205.189.94.9|talk]]) 17:37, 25 September 2023 (UTC)

:there were two uses of "probably" in the article. The 2nd one was unnecessary and I removed it. The remaining one is in the introduction: "[quantum algorithms] might be able to solve some problems faster than classical algorithms because the quantum superposition and quantum entanglement that quantum algorithms exploit ''probably'' cannot be efficiently simulated on classical computers". Here I think "probably" is actually justified (though maybe a better formulation can be found). As I read it, it means to express the fact that it's a logical possibility that quantum mechanics can be efficiently simulated on a classical computer. If that were the case, then any efficient quantum algorithm would give rise (with no more than polynomial overhead) to an efficient classical algorithm and no relevant speedup would be expected. I think it is a widely shared assumption or expectation that it is ''not'' possible to efficiently simulate quantum mechanics (and it is borne out by decades of attempts to find efficient numerical algorithms). An alternative formulation that makes more explicit the current state of knowledge would be: "some [quantum algorithms] are expected to solve their tasks faster than any classical algorithms can, because the many-body quantum entanglement and interference that quantum algorithms exploit cannot be efficiently simulated on classical computers. While no proof of the impossibility of such a efficient classical simulation exists, it is considered very unlikely that such a simulation is feasible in general." (As reference for this "common belief", one could cite John Watrous: "There are several problems known to be in BQP but not known (and generally not believed) to be in BPP.", see {{arXiv|0804.3401}}, p13.) --[[User:Qcomp|Qcomp]] ([[User talk:Qcomp|talk]]) 17:29, 27 September 2023 (UTC)