Step 1: Pick up Nielsen and Chuang, the standard textbook in the field. Step 2: Solve the microsoft Q# Quantum Katas, which take you through basic quantum gates all the way up to quantum algorithms. Step 3: Bedtime read Scott Aaronson's "quantum computing since Democritus" for a great _view_ into the way a researcher in quantum computing thinks about quantum phenomenon, entanglement, and all that.
I _just_ finished a course in college that did this, and I gained a lot from it: A lot of it made me "feel" QM better than the physics courses ever did.
[1] https://mitpress.mit.edu/books/functional-differential-geome...
That said, I agree that SIQM and SICP are totally different (again, I haven't read SICM), and I suspect the similar naming is a coincidence. In my mind, they're linked only by the name and and the qualities I mentioned before (they are two of my favourite books). I read SIQM as a physics undergraduate before I ever heard of SICP, and it has nothing whatsoever to do with computers. As a philosophy professor writing about quantum mechanics, I doubt the author was aware of the existence of SICP, let alone that he was attempting to "ride on its coattails" as the linked comment claims.
Regarding the names, SICP and SIQM use the terms "structure" and "interpretation" in very different ways. In SIQM it's structure in the sense of the mathematical structure of the theory (Hilbert spaces, operators, eigenvalues, etc) and interpretation in the sense of philosophical interpretations (eg. the Copenhagen interpretation. The title is therefore a straightforward description of the two separate sections of the book. With SICP I was never really clear on the meaning of the title, particularly the interpretation part: interpretation by a human or a computer, or is it deliberately ambiguous?
There's also a minor, but telling, difference in the titles: SIQM's title actually starts with "The".
Connecting the math with a physical scenario, and highlighting how your intuitions are wrong, to help you develop new ones.
Feynman's Lectures on Physics starts with the 2 slit experiment, then talks about shining light on the holes to see which hole the electron goes through, then making the energy (wavelength) of the light lower (longer) to try to disturb it less.
Or that you shouldn't think of filters as just removing parts of the wave. For example, put unpolarized light through a vertically polarizing filter, then a horizontally polarized one. No light comes out. Then, in between the two, put a filter at 45 degrees. Now, you do get some light coming out of that horizontal filter.
The math tells you this, of course, but if you don't have an intuitive sense of how that maps to the physical world, you can end up e.g. not noticing where there's a mistake in your calculation that would be obvious it you thought about what it means physically.