References

https://homepages.cwi.nl/~rdewolf/qcnotes.pdf

https://www.researchgate.net/publication/1758552_An_Introduction_to_Quantum_Computing/link/0deec5346d76e62b3d000000/download

# Quantum Mechanics

## 1. Superposition

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.

## 2. Measurement

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.**

## 3. Unitary Evolution

Operator: change a state to another state