Ciro Santilli @cirosantilli  40

Given jointly by the department of Physics of the University of Oxford and the mathematics institute of the University of Oxford.

It is good to see that top-universities is still keeping up with it's main purpose: spontaneous eugenics:

The closest site of the University of California to San Francisco. Berkeley, California is a small town on the East of the San Francisco Bay.

The second one of the University of California after UC Berkeley.

The third one of the University of California after UC Berkeley and UCLA.

A more concrete and easier to understand version of it is the more photon-specific Poincaré sphere, have a look at that one first.

2D representation of $SU(2)$.

The Twelve Apostles were actually officially appointed by Jesus amongst his followers. It was not simply that they were the first followers. It was official rank.

Brother of andrew the Apostle, called by Jesus in fishers of men. Born Simon, but Jesus renamed him to Peter, thus the weird "Simon called Peter" way he is referred to as in some versions of the Bible.

Brother of Saint Peter, called by Jesus in fishers of men. Crucified.

Trapped ion people acknowledge that they can't put a million qubits in on chip (TODO why) so they are already thinking of ways to entangle separate chips. Thinking is maybe the key word here. One of the propoesd approaches inolves optical links. Universal Quantum for example explicitly rejects that idea in favor of electric field link modularity.

Take the group of all Translation in ${\mathbb{R}}^1$.

Let's see how the generator of this group is the derivative operator:

The way to think about this is:

So let's take the exponential map:and we notice that this is exactly the Taylor series of $f(x)$ around the identity element of the translation group, which is 0! Therefore, if $f(x)$ behaves nicely enough, within some radius of convergence around the origin we have for finite $x_0$:

This example shows clearly how the exponential map applied to a (differential) operator can generate finite (non-infinitesimal) Translation!