Bernstein-Vazirani phase kickback
= Bernstein-Vazirani phase kickback
{c}
For $f(x)=a\mathbin\cdot x\mathbin\oplus b$, phase kickback followed by a Walsh-Hadamard transform maps the uniform phase state to
$$
(-1)^b|a\rangle.
$$
The hidden linear string $a$ is therefore recovered with certainty.