trying to elaborate on the OP a little by avoiding math terminology: part 1 here is essentially the idea of logic circuits. you can write these down in terms o

trying to elaborate on the OP a little by avoiding math terminology: part 1 here is essentially the idea of logic circuits. you can write these down in terms of large vectors of 0s and 1s, and operations transforming them as large matrices -- which is useful because it takes familiar ideas (to a CS student) and casts it using mathematical formalisms that are later required for weird quantum stuff. this could be unfamiliar if you haven't learned about matrix/vector multiplication. but ultimately it's just a different way of talking about combinations of AND/OR/NOT on truth values. part 2 just says, go from vectors of 0s and 1s to probabilities between 0 and 1. the "L1 norm" (aka Manhattan or taxicab distance) in this situation just means that all the values together have to sum up to 1, the way probabilities do. this includes part 1 as a special case, and extends it naturally. part 3 is indeed where the weird quantum stuff comes in. no easy explanation, you do have to get an idea of how complex numbers work. but again, the familiar logic circuits of part 1 are still a special case. the "L2 norm" for real numbers is just the regular straight-line distance -- I can't provide a good intuition for complex numbers though.