  The Goldreich-Levin algorithm was originally proposed for a cryptographic
purpose and then applied to learning. The algorithm is to find some larger
Walsh coefficients of an $n$ variable Boolean function. Roughly speaking, it
takes a $poly(n,\frac{1}{\epsilon}\log\frac{1}{\delta})$ time to output the
vectors $w$ with Walsh coefficients $S(w)\geq\epsilon$ with probability at
least $1-\delta$. However, in this paper, a quantum algorithm for this problem
is given with query complexity $O(\frac{\log\frac{1}{\delta}}{\epsilon^4})$,
which is independent of $n$. Furthermore, the quantum algorithm is generalized
to apply for an $n$ variable $m$ output Boolean function $F$ with query
complexity $O(2^m\frac{\log\frac{1}{\delta}}{\epsilon^4})$.
