  We present a quantum algorithm for approximating the linear structures of a
Boolean function $f$. Different from previous algorithms (such as Simon's and
Shor's algorithms) which rely on restrictions on the Boolean function, our
algorithm applies to every Boolean function with no promise. Here, our methods
are based on the result of the Bernstein-Vazirani algorithm which is to
identify linear Boolean functions and the idea of Simon's period-finding
algorithm. More precisely, how the extent of approximation changes over the
time is obtained, and meanwhile we also get some quasi linear structures if
there exists. Next, we obtain that the running time of the quantum algorithm to
thoroughly determine this question is related to the relative differential
uniformity $\delta_f$ of $f$. Roughly speaking, the smaller the $\delta_f$ is,
the less time will be needed.
