References
https://homepages.cwi.nl/~rdewolf/qcnotes.pdf
https://www.researchgate.net/publication/1758552_An_Introduction_to_Quantum_Computing/link/0deec5346d76e62b3d000000/download
Quantum state is a (complex) superposition of classical states.
Here, the coefficients are complex numbers called amplitudes.
The states
are the basis of the N-dimensional Hilbert space.
For example, the state can be spin state, angular momentum, etc.
The (superposed) state is not observable, but the we will see only one of the classical state by "measurement". The probability of measurement to a state, |j>, is the square of the amplitude.
$$ P(j) = |\alpha_j|^2 $$
The measurement is non-unitary, i.e., irreversible.
Operator: change a state to another state