Well, for one, KaTeX doesn't do "LaTeX" but a limited subset of the TeX equation syntax.
As such, it can't handle more complicated macros or typesetting anything apart from equations.
This is not a very good explanation, nor is it useful for anything.
A single qubit is not useful for computation and the way it is written doesn't generalize to more than a single qubit.
The code doesn't even really simulate a single qubit properly, since it doesn't use complex numbers.
What they call a "Rydberg gate" is not a gate at all.
Most of the text feels like it's written by an AI.
I suppose it's since it doesn't really support LaTeX but instead uses MathJax to render equations.
TeX is a a turing-complete language, picking some random subset of LaTeX commands would feel pretty arbitrary to me. In comparison, supporting full markdown syntax is pretty easy.
This protocol depends on multipartite entanglement, so it does seem quite far away from being practical for anything yet.
If quantum routers were a solved problem and we had a quantum internet (last I checked, we do not), for this we would also need some form of 'coherent multicast routing'.
What's done in such an experiment is that we initialize a quantum state in a particular state (that this is possible is not actually obvious, but let's assume it's true) and then we make a lot of repeated measurements after different amounts of times.
So we're not talking about a single system, but instead about statistics about a set of measurements with systems that have been set up in the same initial state. (Each system only being measured once after a certain time after it's being set up).
As a quantum physicist: This might be an interesting experiment, but as far as the theory goes, this is exactly what is to be expected from standard quantum mechanics.
Quantum leaps being instantaneous would be a (possibly common) misconception.
The leap in a quantum leap is describing the notion of a discrete jump in measurement outcomes.
Or if you're already using vim anyway, you can use a plugin like vimtex (https://github.com/lervag/vimtex) which automates the compiling after saving the file.
