Ciro Santilli @cirosantilli 37

Aaron, Ciro Santilli will complete your quest to make eduction free. Just legally this time, with the and with the Creative Commons license you helped to create.

Ciro likes how The Internet's Own Boy (2014) explains how Aaron felt like high school was bullshit, and that he could learn whatever he wanted from books, which is one of Ciro's key feelings.

It also mentions how he was a natural teacher from a very early age.

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 $|00⟩$ and $|01⟩$ should be possible. Therefore, the state must be of the form:where $x$ and $y$ are two complex numbers such that $|x|+|y|=1.0$

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 $|10⟩$ and $|11⟩$ were swapped from $x$ and $y$ to $y$ and $x$ 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.

Ciro Santilli worked on it for a brief time in 2016, when it was still called Ring, before he got fired. :-)

The people were quite nice and the project idea is fine, Ciro hopes they succeed.

The 3D structure of GFP is so cool. It is so clearly a bottle with a fluorescent bit well isolated right in the middle. Like a little lamp.

Nice, nice place. Natural sciences only, no bullshit.

Based on the $L_x$,$L_y$ and $L_z$ derived at Lie algebra of $SO(3)$ we can calculate the Lie bracket as:

See: internal and spacetime symmetries.

Like the special orthogonal group is to the orthogonal group, $SO(m,n)$ is the subset of $O(m,n)$ with determinant equal to exactly 1.

Approximation to Huygens-Fresnel principle.