Let $\mathbb{C}^{2}$ be the \reftext{def:complex-coordinate-space-cn-2026a}{complex coordinate space} with $n=2$, which is a \reftext{def:vector-space-2026a}{complex vector space} by \ref{lem:cn-vector-space-2026a}, equipped with the \reftext{def:standard-inner-product-cn-2026a}{standard inner product}, which is an inner product on it by \ref{lem:standard-inner-product-cn-2026a}.

The \textbf{qubit state space} is this \reftext{def:complex-inner-product-space-2026a}{complex inner product space}. Its \textbf{computational basis vectors} are the elements

of $\mathbb{C}^{2}$, also written $|0\rangle$ and $|1\rangle$ respectively. A \textbf{qubit state vector} is a \reftext{def:unit-vector-2026a}{unit vector} of the qubit state space.