Ciro Santilli @cirosantilli 40

Vs metric:

tmux for newbs: Section "Terminal multiplexers are CLI desktop environments".

Our notation: $D_n$, called "dihedral group of degree n", means the dihedral group of the regular polygon with $n$ sides, and therefore has order $2n$ (all rotations + flips), called the "dihedral group of order 2n".

A Cartesian product that carries over some extra structure of the input groups.

E.g. the direct product of groups carries over group structure on both sides.

Contains the gene: e. Coli K-12 MG1655 gene thrL.

Subset of the longer E. Coli K-12 MG1655 transcription unit thrLABC.

Like the U.S.' spring term.

Knock knock.

Does not have any non-trivial normal subgroup.

And therefore, going back to our intuition that due to the fundamental theorem on homomorphisms there is one normal group per homomorphism, a simple group is one that has no non-trivial homomorphisms.

We don't need to understand a super generalized version of tensor products to know what they mean in basic quantum computing!

Intuitively, taking a tensor product of two qubits simply means putting them together on the same quantum system/computer.

When we write the bra-ket notation: $|00⟩$ that is the same as $|0⟩\otimes |0⟩$.

The tensor product is called a "product" because it distributes over addition.

E.g. consider:

Intuitively, in this operation we just put a Hadamard gate qubit together with a second pure $|0⟩$ qubit.

And the outcome still has the second qubit as always 0, because we haven't made them interact.

The quantum state $\frac{|00⟩+|10⟩}{\sqrt{2}}$ is called a separable state, because it can be written as a single product of two different qubits. We have simply brought two qubits together, without making them interact.

If we then add a CNOT gate to make a Bell state:we can now see that the Bell state is non-separable: we've made the two qubits interact, and there is no way to write this state with a single tensor product. The qubits are fundamentally entangled.

Bibliography:

An inner product $x\cdot y$ induces a norm with:

Studies biology from a more global point of view, if putting all little pieces of an organism make up the final biological function.

Some key activities:

The OS that the Gods ordered be made.

One is reminded of Ulillillia, see also: www.youtube.com/watch?v=9-79yOZ13qg The Story of Ulillillia by Atrocity Guide (2019)

We are all somewhere in the spectrum.