Quantum logic gates are needed because you can't compute the matrix explicitly as it grows exponentially by 
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01One key insight, is that the matrix of a non-trivial quantum circuit is going to be huge, and won't fit into any amount classical memory that can be present in this universe.
This is because the matrix is exponential in the number qubits, and is more than the number of atoms in the universe!
Therefore, off the bat we know that we cannot possibly describe those matrices in an explicit form, but rather must use some kind of shorthand.
But it gets worse.
This is because knowing the matrix, basically means knowing the probability result for all possible outputs for each of the possible inputs.
But if we had those probabilities, our algorithmic problem would already be solved in the first place! We would "just" go over each of those output probabilities (OK, there are of those, which is also an insurmountable problem in itself), and the largest probability would be the answer.
So if we could calculate those probabilities on a classical machine, we would also be able to simulate the quantum computer on the classical machine, and quantum computing would not be able to give exponential speedups, which we know it does.
To see this, consider that for a given input, say and therefore when you multiply it by the unitary matrix of the quantum circuit, what you get is the first column of the unitary matrix of the quantum circuit. And
000 on a 3 qubit machine, the corresponding 8-sized quantum state looks like:000 -> 1000 0000 == (1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)001, gives the second column and so on.As a result, to prove that a quantum algorithm is correct, we need to be a bit smarter than "just calculate the full matrix".
Which is why you should now go and read: Section "Quantum algorithm".
This type of thinking links back to how physical experiments relate to quantum computing: a quantum computer realizes a physical experiment to which we cannot calculate the probabilities of outcomes without exponential time.
So for example in the case of a photonic quantum computer, you are not able to calculate from theory the probability that photons will show up on certain wires or not.
T.H. Tse is a computer scientist known for his work in software engineering, formal methods, and the analysis of programming languages. He has significantly contributed to areas such as program verification, type systems, and software reliability. Notably, he is a professor at The University of Hong Kong and has published numerous scholarly articles and research papers in these fields. If you're looking for something specific about T.H.
Quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925) by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01This Heisenberg's breakthrough paper on matrix mechanics which later led to the Schrödinger equation, see also: history of quantum mechanics.
Published on the Zeitschrift für Physik volume 33 page pages 879-893, link.springer.com/article/10.1007%2FBF01328377
Modern overview: www.mat.unimi.it/users/galgani/arch/heisenberg25amer_j_phys.pdf
"Software by year" typically refers to the categorization or listing of software that was released or became significant in a particular year. This can encompass a wide range of software types, including operating systems, applications, programming languages, video games, and more. To illustrate how software has evolved over the years, here are a few notable examples from various years: ### 1970s - **1971**: The first version of the Unix operating system.
The Elektronika BK operating systems are a family of operating systems designed for the Elektronika BK series of computers, which were developed in the Soviet Union during the 1980s. These computers were based on the Soviet-made microprocessor, the K580, which was similar to the Intel 8080 and Zilog Z80.
.su is a country code top-level domain (ccTLD) that was originally assigned to the Soviet Union (USSR). Although the Soviet Union dissolved in 1991, the .su domain was retained and is still in use today. It is managed by the "Russian Institute for Public Networks" (RIPN). Over the years, .
Quantum numbers appear directly in the Schrödinger equation solution for the hydrogen atom.
However, it very cool that they are actually discovered before the Schrödinger equation, and are present in the Bohr model (principal quantum number) and the Bohr-Sommerfeld model (azimuthal quantum number and magnetic quantum number) of the atom. This must be because they observed direct effects of those numbers in some experiments. TODO which experiments.
E.g. The Quantum Story by Jim Baggott (2011) page 34 mentions:This refers to forbidden mechanism. TODO concrete example, ideally the first one to be noticed. How can you notice this if the energy depends only on the principal quantum number?
As the various lines in the spectrum were identified with different quantum jumps between different orbits, it was soon discovered that not all the possible jumps were appearing. Some lines were missing. For some reason certain jumps were forbidden. An elaborate scheme of ‘selection rules’ was established by Bohr and Sommerfeld to account for those jumps that were allowed and those that were forbidden.
Quantum Numbers, Atomic Orbitals, and Electron configurations by Professor Dave Explains (2015)
Source. He does not say the key words "Eigenvalues of the Schrödinger equation" (Which solve it), but the summary of results is good enough.The 1801 series refers to a family of microprocessors developed in the Soviet Union during the late 1970s and early 1980s. The design of these CPUs is based on the earlier 8080 architecture from Intel and they were used in various computing and embedded systems within the Soviet Union. One of the most notable processors in the 1801 series is the K1801VM1, which is a 16-bit microprocessor that supports integer and some floating-point operations.
"Analitik" can refer to several concepts depending on the context, but it is commonly associated with the following areas: 1. **Analytics**: In a broad sense, "analitik" may refer to the field of analytics, which involves the systematic computational analysis of data. This encompasses various forms of data analysis, including business analytics, data analytics, and statistical analytics, aimed at gaining insights and informing decision-making processes.
As of my last knowledge update in October 2021, Angstrem is a company known for its focus on microelectronics and semiconductor manufacturing. It is involved in producing integrated circuit components and technologies, often catering to markets such as telecommunications, automotive, and consumer electronics. The company may have its roots in a historical context relating to the semiconductor industry, possibly with connections to advancements in chip technology.
Computer Russification refers to the process of adapting computer software, applications, and systems to be compatible with the Russian language and culture. This can involve several steps, including: 1. **Localization of Software**: This includes translating the user interface, documentation, and help files from other languages into Russian. It also involves adjusting date formats, currency, and other regional settings.
There seems to be nothing of particular artistic value as far as we've seen so far, the only interest in such tokens seems to be that:
- there are some examples that came earlier than those in the Bitcoin blockchain, notably a bit earlier than Section "BitLen"
- Namecoin is a NFT system unlike Bitcoin which is fungible, so those assets are naturally tradable
The Staden Package is a collection of programs and tools designed for the analysis and manipulation of DNA and protein sequences. It was developed primarily for the purpose of processing and analyzing sequence data obtained from DNA sequencing technologies. The package is named after the city of Staden, where the project originated in the 1980s.
The term "social genome" typically refers to the complex interplay of social factors, behaviors, and characteristics that shape individual and collective social experiences. While it can vary based on context, it often encompasses elements such as social networks, relationships, cultural influences, and the impact of socioeconomic status on behavior and outcomes in society.
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