The post [and me, since I wrote it] recommends the video series Quantum Computing for the Determined [1].
If you're more familiar with physics than programming, Leonard Susskind's 'Quantum Mechanics: The Theoretical Minimum' [2] might work better. But I agree with Scott Aaronson that learning about quantum information before learning about quantum physics is easier than the opposite direction [3]:
> There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. [...]
> Today, in the quantum information age, the fact that all the physicists had to learn quantum this way seems increasingly humorous. For example, I've had experts in quantum field theory -- people who've spent years calculating path integrals of mind-boggling complexity -- ask me to explain the Bell inequality to them. That's like Andrew Wiles asking me to explain the Pythagorean Theorem. [...]
> The second way [...] starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs.
> But I agree with Scott Aaronson that learning about quantum information before learning about quantum physics is easier than the opposite direction.
I'm unconvinced that this is anything but Scott's personal opinion. Basically all teaching methodology advocates for concrete examples over abstract concepts. You can't get much more abstract than generalization of probability theory to allow minus signs.
It might work well for some people, and I'm happy it worked for you.
I don't really think the physical approach is any more concrete than Scott Aaronson's approach (at least in the way most people talk about concreteness wrt pedagogy). The point of having examples is to illustrate how general principles work in practice by specializing. You can do this just fine in quantum information/computation by discussing particular algorithms, problems, etc.
Frankly having taken both QC courses and QM courses, I found the physics-oriented exposition used a bunch of verbiage to phrase things in an experimental/physical way without really specializing the mathematical objects in any sense (eg, Stern-Gerlach experiments). That particular sort of concreteness can be helpful in other parts of physics, but physical intuition is weak to nonexistent in QM.
Anyway, I'm nowhere near a physicist so take my review with a grain of salt.
In the case of QM, I think the concrete physical cases are all counter-intuitive. They trigger the wrong ideas and confuse people instead of helping them, e.g. by having them focus on malformed questions like "is it a particle or is it a wave?".
Which is not to say that I think you should do two years of linear algebra before understanding how the heck it applies to reality. That would also be insane. I guess I just think that the first concrete case should be a qubit simulator. Something grounded that you can come back to and say "Well, what if I did this?" and get the right answer.
The IBM IQE simulator, that the article mentions (somewhat derisively), actually has a good tutorial on the topic. I found that IQE, since it is actually designed to run on an actual quantum computer, to be the most helpful thing I've done to understand how you would actually program a quantum computer. Most of the other simulators provide additional information that's not accessible on an actual quantum computer, making it harder to separate convenient "debugger" functionality from what is actually doable. Plus, by it's nature, IQE talks about the actual challenges and effects of noise on the output; and why quantum error correction is critical. Also, IQE gives numerous trivial example circuits, that for some reason helped things click for me.
A real quantum computer wins by a long shot in terms of coolness and difficulty to construct... But at this point there's no performance increase and they should provide the same results as a simulator. So I'll take the instantaneous results that a simulator provides until the hardware catches up.
It's mostly just complex linear algebra, finite dimensional. So, think eigenvectors, eigenvalues and operators. Measurements are essentially projection operators. And a little more tricky: the tensor product. The tensor product is the physicists way of saying "and". The Bloch sphere is a clever way of notating a vector. You may need density matrices (aka density operators), that's a bit more involved, but basically it allows you to take a probability distribution over vectors.
