Ciro Santilli @cirosantilli 37

The dominating model of a computer.

The model is extremely simple, but has been proven to be able to solve all the problems that any reasonable computer model can solve, thus its adoption as the "default model".

The smallest known Turing machine that cannot be proven to halt or not as of 2019 is 7,918-states: www.scottaaronson.com/blog/?p=2725. Shtetl-Optimized by Scott Aaronson is just the best website.

A bunch of non-reasonable-looking computers have also been proven to be Turing complete for fun, e.g. Magic: The Gathering.

The third part module, which clutters up any serches you make for the built-in one.

If looking through these don't make you think of the Book of Genesis then nothing will.

Encryption algorithms that run on classical computers that are expected to be resistant to quantum computers.

This is notably not the case of the dominant 2020 algorithms, RSA and elliptic curve cryptography, which are provably broken by Grover's algorithm.

However, as of 2020, we don't have any proof that any symmetric or public key algorithm is quantum resistant.

Post-quantum cryptography is the very first quantum computing thing at which people have to put money into.

The reason is that attackers would be able to store captured ciphertext, and then retroactively break them once and if quantum computing power becomes available in the future.

There isn't a shade of a doubt that intelligence agencies are actively doing this as of 2020. They must have a database of how interesting a given source is, and then store as much as they can given some ammount of storage budget they have available.

A good way to explain this to quantum computing skeptics is to ask them:Post-quantum cryptography is simply not a choice. It must be done now. Even if the risk is low, the cost would be way too great.

Group of the unitary matrices.

Complex analogue of the orthogonal group.

One notable difference from the orthogonal group however is that the unitary group is connected "because" its determinant is not fixed to two disconnected values 1/-1, but rather goes around in a continuous unit circle. $U(1)$ is the unit circle.