  In this paper, we give a quantum circuit that calculates symmetrized
functions. Our algorithm applies the original Grover's algorithm or a variant
thereof such as AFGA (adaptive fixed point Grover's algorithm). Our algorithm
uses AFGA in conjunction with two new techniques we call "targeting two
hypotheses" and "blind targeting". Suppose AFGA drives the starting state
$|s\rangle$ to the target state $|t\rangle$. When targeting two hypotheses,
$|t\rangle$ is a superposition $a_0|0\rangle + a_1|1\rangle$ of two orthonormal
states or hypotheses $|0\rangle$ and $|1\rangle$. When targeting blindly, the
value of $\langle t| s\rangle$ is not known a priori.
