One important area of research and development of quantum computing is the development of benchmarks that allow us to compare different quantum computers to decide which one is more powerful than the other.
Ideally, we would like to be able to have a single number that predicts which computer is more powerful than the other for a wide range of algorithms.
However, much like in CPU benchmarking, this is a very complex problem, since different algorithms might perform differently in different architectures, making it very hard to sum up the architecture's capabilities to a single number as we would like.
The only thing that is directly comparable across computers is how two machines perform for a single algorithm, but we want a single number that is representative of many algorithms.
For example, the number of qubits would be a simple naive choice of such performance predictor number. But it is very imprecise, since other factors are also very important:
Quantum volume is another less naive attempt at such metric.
Indefinite special orthogonal group by 
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Like the special orthogonal group is to the orthogonal group, is the subset of with determinant equal to exactly 1.
Generalization of orthogonal group to preserve different bilinear forms. Important because the Lorentz group is .
General Game Playing (Stanford project) by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01This kind of died at some point checked as of 2023.
In order to create a test user with password instead of peer authentication, let's create test user:
createuser -P user0
createdb user0-P makes it prompt for the users password.Alternatively, to create the password non-interactively stackoverflow.com/questions/42419559/postgres-createuser-with-password-from-terminal:Can't find a way using the
psql -c "create role NewRole with login password 'secret'"createuser helper.We can then login with that password with:which asks for the password we've just set, because the
psql -U user0 -h localhost-h option turns off peer authentication, and turns off password authentication.The password can be given non-interactively as shown at stackoverflow.com/questions/6405127/how-do-i-specify-a-password-to-psql-non-interactively with the
PGPASSWORD environment variable:PGPASSWORD=a psql -U user0 -h localhostNow let's create a test database which
user0 can access with an existing superuser account:createdb user0db0
psql -c 'GRANT ALL PRIVILEGES ON DATABASE user0db0 TO user0'We can check this permission with:which now contains:The permission letters are explained at:
psql -c '\l' List of databases
Name | Owner | Encoding | Collate | Ctype | Access privileges
-----------+----------+----------+-------------+-------------+-----------------------
user0db0 | ciro | UTF8 | en_GB.UTF-8 | en_GB.UTF-8 | =Tc/ciro +
| | | | | ciro=CTc/ciro +
| | | | | user0=CTc/cirouser0 can now do the usual table operations on that table:PGPASSWORD=a psql -U user0 -h localhost user0db0 -c 'CREATE TABLE table0 (int0 INT, char0 CHAR(16));'
PGPASSWORD=a psql -U user0 -h localhost user0db0 -c "INSERT INTO table0 (int0, char0) VALUES (2, 'two'), (3, 'three'), (5, 'five'), (7, 'seven');"
PGPASSWORD=a psql -U user0 -h localhost user0db0 -c 'SELECT * FROM table0;'The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.
Implosion-type fission weapons are more complicated than gun-type fission weapon because you have to precisely coordinate the detonation of a bunch of explosives.
A cool thought: bacteria like E. Coli replicate every 20 minutes. A human replicates every 15 years. So how can multicellular beings possibly cope with the speed of evolution of parasites?
The answer is that within us, the adaptive immune system is a population of cells that evolves very quickly. So in a sense, within our bodies there is fast cell-level non-inheritable evolution happening daily!
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact