It looks good! I think it explains the ideas pretty clearly!

How about getting Jacob or someone to polish the English? I could do it too, but I'm sort of crazy-busy right now, and I'd prefer to make the next more sophisticated layer of improvements _after_ the grammar and typos are fixed.

I'm talking about things like these:

"State of electron can be described as complex, two-dimensional vector" $\mapsto$

"**A** state of **an** electron can be described as **a** complex, two-dimensional vector"

"Energy, and evolution, of this state is described by a Hamiltionian:" $\mapsto$

"**The** energy, and evolution, of this state is described by a **Hamiltonian**:"

"How to add classically quantum things" $\mapsto$

"How to **classically add** quantum things" (This may not technically be grammatical, but it's what people would actually say. The other one makes me think you're talking about "classically quantum things".)

and so on (about 50 more). After these changes are made, I can make the more sophisticated edits while staying happy. There's nothing worse than a grumpy editor!