Solution (source code)

= Solution

Starting from the $n$-qubit <computational basis> state $|0\rangle^{\otimes n}$, apply one <Hadamard gate> to every qubit. Since $H|0\rangle=(|0\rangle+|1\rangle)/\sqrt2$,
$$
H^{\otimes n}|0\rangle^{\otimes n}
=\frac1{\sqrt{2^n}}(|0\rangle+|1\rangle)^{\otimes n}
=\frac1{\sqrt{2^n}}\sum_{x\in B_n}|x\rangle
=\boxed{|\psi_n\rangle}.
$$
\b[Thus parallel Hadamard gates prepare the <uniform quantum superposition>.]