One of the many thing that confuse me in the field of QC is what makes the measurement of a qubit in a quantum computer any different than just choosing at random (in a classical computer) (that's not my actual question)
Suppose I have $n$ qubits, and my state is a vector of their amplitudes $(a_1,a_2,\dots,a_n)^\mathrm{T}$.1
If I pass that state through some gates and do all sorts of quantum operations (except for measurement), and then I measure the state. I'll only get one of the options (with varying probabilities).
So where's the difference between doing that, and generating a number randomly from some convoluted/complicated distribution? What makes quantum computations essentially different from randomized classical ones?
- I hope I didn't misunderstand how states are represented. Confused about that, as well...