Walsh-Hadamard transform
= Walsh-Hadamard transform
{c}
{title2=$H^{\otimes n}$}
{wiki=Hadamard_transform}
On $n$ qubits, the Walsh-Hadamard transform satisfies
$$
H^{\otimes n}|x\rangle
=2^{-n/2}\sum_{y\in\{0,1\}^n}(-1)^{x\cdot y}|y\rangle,
$$
where the dot product is evaluated modulo two.