Ciro Santilli @cirosantilli 40

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.

MOOCs are a bad idea. We don't want to simply map the pre-computer classroom to the Internet. The Internet allows, and requires, fundamentally new ways to do things. More like Stack Overflow/Wikipedia. More like OurBigBook.com.