accounts for them all, which we know how to do due to the classification of finite fields.
So we see that the classification is quite simple, much like the classification of finite fields, and in strict opposition to the classification of finite simple groups (not to mention the 2023 lack of classification for non simple finite groups!)
Clifford gates by Ciro Santilli 40 Updated 2025-07-16
This gate set alone is not a set of universal quantum gates.
Notably, circuits containing those gates alone can be fully simulated by classical computers according to the Gottesman-Knill theorem, so there's no way they could be universal.
This means that if we add any number of Clifford gates to a quantum circuit, we haven't really increased the complexity of the algorithm, which can be useful as a transformational device.
You are nothing but useless leeches in the Internet age.
You must go bankrupt all of you, ASAP.
Fuck Elsevier, fuck Springer, and fuck all the like.
Research paid with taxpayer money must be made available for free.
Researchers and reviewers all work for peanuts, while academic publishers get money for doing the work that an algorithm could do. OurBigBook.com.
When Ciro learned URLs such as www.nature.com/articles/181662a0 log you in automatically by IP, his mind blew! The level of institutionalization of this theft is off the charts! The institutionalization of theft is also clear from article prices, e.g. 32 dollars for a 5 page article.
Key physics papers from the 50's are still copyright encumbered as of 2020, see e.g. Lamb-Retherford experiment. Authors and reviewers got nothing for it. Something is wrong.
Infinite list of other people:
  • blog.machinezoo.com/public-domain-theft by Robert Važan:
    Scientific journals are perhaps one of the most damaging IP rackets. Scientists are funded by governments to do research and publish papers. Reviews of these papers are done by other publicly funded scientists. Even paper selection and formatting for publication is done by scientists. So what do journals actually do? Nearly nothing.
Video 1.
Academic Publishing by Dr. Glaucomflecken (2022)
Source.
Ciro Santilli can accept closed source on server products more easily than offline, because the servers have to be paid for somehow (by stealing your private data).
Closed source on offline products used by millions of people is evil, when you could just have those for free with open source software! Thus Ciro's hatred for Microsoft Windows and MacOS (at least userland, maybe).
Closed standard by Ciro Santilli 40 Updated 2025-07-16
ISO is the main culprit of this bullshit, some notable examples related to open source software:
The only low level thing that escaped this was OpenGL via Khronos, what heroes those people are.
How the hell are you supposed to develop an open source implementation of something that has a closed standard?
Not to mention open source test suites, that would be way too much to ask for, those always end up being made by some shady small companies that go bankrupt from time to time, see e.g. .
There's no point.
The question remains there, but people lose the ability to help the asker.
Reputation is meaningless regardless, since JavaScript gurus will always have 1000x more readers than low level junkies.
The deeper problem: the existence of multiple separate websites instead of just using the tags on a single website.
Closurism by Ciro Santilli 40 Updated 2025-07-16
Closurism is a term invented by Ciro Santilli to refer to content moderation policies that lock threads in online forums, preventing people from adding new comments from that point onward.
This is similar to deletionism but a bit less worse, as the pre-existing content is maintained. But new relevant content that comes up cannot be added in the future, so it is still bad.
The outcome of closurism is that new forum posts must then be made about up-to-date aspects of the topic. But then those may fail to reach the same PageRank, so most people never get the new information, or create new posts leading to useless duplication of work.
CNOT gate by Ciro Santilli 40 Updated 2025-07-16
The CNOT gate is a controlled quantum gate that operates on two qubits, flipping the second (operand) qubit if the first (control) qubit is set.
This gate is the first example of a controlled quantum gate that you should study.
To understand why the gate is called a CNOT gate, you should think as follows.
First let's produce a generic quantum state vector where the control qubit is certain to be 0.
On the standard basis:
we see that this means that only and should be possible. Therefore, the state must be of the form:
where and are two complex numbers such that
If we operate the CNOT gate on that state, we obtain:
and so the input is unchanged as desired, because the control qubit is 0.
If however we take only states where the control qubit is for sure 1:
Therefore, in that case, what happened is that the probabilities of and were swapped from and to and respectively, which is exactly what the quantum NOT gate does.
So from this we understand more concretely what "the gate only operates if the first qubit is set to one" means.
Now go and study the Bell state and understand intuitively how this gate is used to produce it.

Pinned article: 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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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