> In a classical word, a qbit is simply a bit and you only have to chose between the 0 or 1 state and simulate it. In a quantum word, you must simulate both.

Not just "both", you have to consider all quantum states.

It is more like adding an imaginary component to a real probability making it a complex probability. It is possible to calculate with the complex probabilities and only collapse to the field of R in the end.