Scott Aaronson has a good point of view that one of the better ways to teach QM is as probability theory generalized to complex numbers. I learned it the old-fashioned physics way, but I have more of a programming mindset, so it probably would have made more sense starting from the quantum information approach.
I think the real mind-blowing thing is that most of quantum computing can be described as applying a unitary matrix operation to some state vector and computing the result. The rest of the field is just about what those unitary operations are and how you chain them together. (Oh... and the whole engineering problem of actually building a machine that does that without decoherence)
well, in that sense the op was saying disregard the real factors of complex numbers, use only 1 and i.
In sum, I interpret that as a start from binary probability. The bayesian rule for example follows trivially from Laplacian equal-chance decision trees, so I think that's a good hint. Does the bayesian/frequentist distinction play a role here (I'd like to think it's not a fundamental distinction, but I really don't know).
> well, in that sense the op was saying disregard the real factors of complex numbers, use only 1 and i.
This is incorrect. The quantum mechanics of discrete systems still requires the use of the continuous field of complex numbers for the amplitudes of different configurations (not just the fourth roots of unity or anything like that). The "discrete" refers to the discreteness of the configuration space (e.g., the discrete spin of an electron, in contrast to the continuous position x of a particle).
Very analogously, one can do classical probability theory for discrete (e.g., binary) outcomes or continuous ones, but either way you need to use the continuous interval between 0 and 1 to represent probabilities for those outcomes. Restricting to binary probabilities (i.e., true or false) would be classical logic, a subset of probability theory.
(It's possible to work with an equivalent formulation of quantum mechanics with only real numbers, rather than complex amplitudes, but these numbers must still be continuous and allowed to go negative. The Wigner representation is an example.)
Incidentally, mixing up the continuity of the amplitude with the continuity of configurations is exactly the sort of mistake it's easy to make when these things are introduced simultaneously! So your misconception is exceedingly reasonable.
I think the real mind-blowing thing is that most of quantum computing can be described as applying a unitary matrix operation to some state vector and computing the result. The rest of the field is just about what those unitary operations are and how you chain them together. (Oh... and the whole engineering problem of actually building a machine that does that without decoherence)