State Space (Quantum Computing)

quantum-computing

Definition

State Space (Quantum Computing)

The state space of a quantum system is a complex Hilbert space $\mathcal{H}$.

Examples

Single Qubit

The state space is ${\mathbb{C}}^2$, with basis $\{|0⟩,|1⟩\}$. A general state is

$$|\psi ⟩=\alpha |0⟩+\beta |1⟩$$

with $|\alpha {|}^2+|\beta {|}^2=1$.