= Fourier sample
{c}
{title2=$\Pr(c)=|\langle c|F|\psi\rangle|^2$}
A Fourier sample is a <computational-basis measurement> outcome after applying a <quantum Fourier transform> $F$ to a <quantum state> $|\psi\rangle$. 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>.
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