A Visual Exploration of the Qubit State

Two-dimensional quantum system

The qubit is a two-dimensional quantum system. Each dimension is denoted by a standard basis vector:

$|0\rangle = \begin{bmatrix}1\\0\end{bmatrix}$, in Python [1, 0] and

$|1\rangle = \begin{bmatrix}0\\1\end{bmatrix}$, in Python [0, 1].

The superposition of both dimensions represents the state of the qubit. This is the qubit state vector $|\psi\rangle$ (“psi”).

$\mathrm{\mid }\psi ⟩=\alpha \mathrm{\mid }0⟩+\beta \mathrm{\mid }1⟩=[$ ...