Basis State (Quantum Computing)

quantum-computing

Definition

Basis State (Quantum Computing)

A basis state of an $n$-qubit system is an element of the computational basis $\{|0⟩,|1⟩{\}}^{\otimes n}$, i.e. a state of the form

$$|b⟩=|b_1⟩\otimes |b_2⟩\otimes \cdots \otimes |b_n⟩$$

with $b_i\in \{0,1\}$, and $\otimes$ denoting the tensor product. The $2^n$ basis states are orthonormal and span the state space ${\mathbb{C}}^{2^n}$.

Example

$n=1$

$|0⟩,|1⟩$.

$n=2$

$|00⟩,|01⟩,|10⟩,|11⟩$

$n=3$

$|000⟩,|001⟩,|010⟩,|011⟩,|100⟩,|101⟩,|110⟩,|111⟩$.