Fourier sample ($\mathrm{Pr}(c)=|⟨c|F|\psi ⟩{|}^2$)

A Fourier sample is a computational-basis measurement outcome after applying a quantum Fourier transform $F$ to a quantum state $|\psi ⟩$. Its distribution is given by the squared Fourier amplitudes. For a uniform periodic coset of spacing $r\mid N$, samples are the multiples $sN/r$ with uniform $s\in {\mathbb{Z}}_r$. Samples need not individually reveal the whole period: a greatest common divisor can remove factors from a single reduced denominator, motivating two-sample exact period recovery.