basis

Quantum computation manipulates vector spaces.
A qubit is a 2 dimensional space.
|> = a |0>+ ß |1> avec |a|² + |ß|² = 1

The state space of a composite system is the tensor product of individual spaces.
|12> = |1>|2>

The evolution of a closed system is represented by a unitary matrix.
|(0)> -> |(t)> = U(t,0) |(0)>

When we measure a qubit we get one of the eigenvector with a probability equal to the squares of the coefficient magnitude.
|> = a |0>+ ß |1> : probability of measuring |0> is |a|²