Quantum algorithm vs quantum gate vs quantum circuit by 
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01There is no fundamental difference between them, a quantum algorithm is a quantum circuit, which can be seen as a super complicated quantum gate.
Perhaps the greats practical difference is that algorithms tend to be defined for an arbitrary number of N qubits, i.e. as a function for that each N produces a specific quantum circuit with N qubits solving the problem. Most named gates on the other hand have fixed small sizes.
Metric created by IonQ.
is the largest number of 1's written by a halting -state Turing machine on a tape initially filled with 0's.
The Busy beaver scale allows us to gauge the difficulty of proving certain (yet unproven!) mathematical conjectures!
To to this, people have reduced certain mathematical problems to deciding the halting problem of a specific Turing machine.
A good example is perhaps the Goldbach's conjecture. We just make a Turing machine that successively checks for each even number of it is a sum of two primes by naively looping down and trying every possible pair. Let the machine halt if the check fails. So this machine halts iff the Goldbach's conjecture is false! See also Conjecture reduction to a halting problem.
Therefore, if we were able to compute , we would be able to prove those conjectures automatically, by letting the machine run up to , and if it hadn't halted by then, we would know that it would never halt.
Of course, in practice, is generally uncomputable, so we will never know it. And furthermore, even if it were computable, it would take a lot longer than the age of the universe to compute any of it, so it would be useless.
However, philosophically speaking at least, the number of states of the equivalent Turing machine gives us a philosophical idea of the complexity of the problem.
The busy beaver scale is likely mostly useless, since we are able to prove that many non-trivial Turing machines do halt, often by reducing problems to simpler known cases. But still, it is cute.
But maybe, just maybe, reduction to Turing machine form could be useful. E.g. The Busy Beaver Challenge and other attempts to solve BB(5) have come up with large number of automated (usually parametrized up to a certain threshold) Turing machine decider programs that automatically determine if certain (often large numbers of) Turing machines run forever.
So it it not impossible that after some reduction to a standard Turing machine form, some conjecture just gets automatically brute-forced by one of the deciders, this is a path to
Being Brazilian, Ciro Santilli is particularly curious about the existence of a Brazilian-focused website one mentioned in the article, as well as in other democracies.
WTF the CIA was doing in Brazil in the early 2010s! Wasn't helping to install the Military dictatorship in Brazil enough!
Here are the democracies found so far, defining a democracy as a country with score 7.0 or more in the Democracy index 2010. In native language:In English, so more deniable:"Almost democracies":Ciro couldn't help but feel as if looking through the Eyes of Sauron himself!
- Germany(2: dedrickonline.com, neighbour-news.com)
- France (4: guide-daventure.com, lesummumdelafinance.com, football-de-luxe.com, suparakuvi.com)
- Italy (2: attivitaestremi.com, podisticamondiale.com)
- Spain (2: armashoy.com, montanismoaventura.com)
- Brazil (1: noticiasmusica.net)
- South Korea (1: economicnewsbuzz.com)
- Poland (1: boxingstop.net)
- Japan (1: snapnewsfront.net)
- Canada (2: kanata-news.com, mynewscheck.com)
- Philippines (1: half-court.net)
- India (1: amishkanews.com)
- Croatia (1: stara-turistick.com)
- Thailand (1: thefairwaysaregreen.com)
- Peru (1: todosperuahora.com)
It is worth noting that democracies represent just a small minority of the websites found. The Middle East, and Spanish language sites (presumably for Venezuela + war on drugs countries?) where the huge majority. But Americans have to understand that democracies have to work together and build mutual trust, and not spy on one another. Even some of the enlightened people from Hacker News seem to not grasp this point. The USA cannot single handedly maintain world order as it once could. Collaboration based on trust is the only way.
Snowden's 2013 revelations particularly shocked USA allies with the fact that they were being spied upon, and as of the 2020's, everybody knows this and has "stopped caring", and or moved to end-to-end encryption by default. This is beautifully illustrated in the Snowden when Snowden talks about his time in Japan working for Dell as an undercover NSA operative:
NSA wanted to impress the Japanese. Show them our reach. They loved the live video from drones. This is Pakistan right now [video shows CIA agents demonstrating drone footage to Japanese officials]. They were not as excited about that we wanted their help to spy on the Japanese population. They said it was against their laws.We bugged the country anyway, of course.And we did not stop there. Once we had their communications we continued with the physical infrastructure. We sneaked into small programs in their power grids, dams, hospitals. The idea was that if Japan one day was not our allies we could turn off the lights.
Another noteworthy scene from that movie is Video "Aptitude test scene from the Snowden 2016 film", where a bunch of new CIA recruits are told that:
Each of you is going to build a covert communications network in your home city [i.e. their fictitious foreign target location written on each person's desk, not necessarily where they were actually born], you're going to deploy it, backup your site, destroy it, and restore it again.
The prototypical example is the Busy beaver function, which is the easiest example to reach from the halting problem.
Well-capitalized Seattle start-up seeks Unix developers by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01Apparently posted to
ba.jobs.offered Usenet newsgroup?Jeff's email was
bezos@netcom.com at the time.www.nature.com/articles/d41586-023-02600-xThey overreached it seems.
Almost since it began, however, the HBP has drawn criticism. The project did not achieve its goal of simulating the whole human brain — an aim that many scientists regarded as far-fetched in the first place. It changed direction several times, and its scientific output became “fragmented and mosaic-like”, says HBP member Yves Frégnac
Sample implementations:
Publicly released documents from the Los Alamos National Laboratory are marked with this identifier. This is for example the case of each video on ther YouTube channel: www.youtube.com/@LosAlamosNationalLab. E.g. Video "Historic, unique Manhattan Project footage from Los Alamos by Los Alamos National Lab" is marked with "LA-UR 11-4449".
www.osti.gov/biblio/1372821 contains "How to Get an LA-UR: Using RASSTI to Release Your Work" which is of interest: permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-17-26023. That document documents the acronym's expansion, plus it leaks some internal-only URLs such as lasearch.lanl.gov/oppie/service.
TODO is there somewhere you can search for the document for a given identifier? Some PDFs are listed at: sgp.fas.org/othergov/doe/lanl/index2b.html
To get an intuition for it, see the sample computation at: en.wikipedia.org/w/index.php?title=Ackermann_function&oldid=1170238965#TRS,_based_on_2-ary_function where in this context. From this, we immediately get the intuition that these functions are recursive somehow.
Quantum computer physical implementation by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01Lists of the most promising implementations:
As of 2020, the hottest by far are:
How To Build A Quantum Computer by Lukas's Lab (2023)
Source. Super quick overview of the main types of quantum computer physical implementations, so doesn't any much to a quick Google.
He says he's going to make a series about it, so then something useful might actually come out. The first one was: Video "How to Turn Superconductors Into A Quantum Computer by Lukas's Lab (2023)", but it is still too basic.
The author's full name is Lukas Baker, www.linkedin.com/in/lukasbaker1331/, found with Google reverse image search, even though the LinkedIn image is very slightly different from the YouTube one.
Quantum Computation and Quantum Information by Nielsen and Chuang by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01The last value we will likely every know for the busy beaver function! BB(6) is likely completely out of reach forever.
By 2023, it had basically been decided by the The Busy Beaver Challenge as mentioned at: discuss.bbchallenge.org/t/the-30-to-34-ctl-holdouts-from-bb-5/141, pending only further verification. It is going to be one of those highly computational proofs that will be needed to be formally verified for people to finally settle.
As that project beautifully puts it, as of 2023 prior to full resolution, this can be considered the:on the Busy beaver scale.
simplest open problem in mathematics
There are unlisted articles, also show them or only show them.