  A general quantum search algorithm aims to evolve a quantum system from a
known source state $|s\rangle$ to an unknown target state $|t\rangle$. It uses
a diffusion operator $D_{s}$ having source state as one of its eigenstates and
$I_{t}$, where $I_{\psi}$ denotes the selective phase inversion of
$|\psi\rangle$ state. It evolves $|s\rangle$ to a particular state $|w\rangle$,
call it w-state, in $O(B/\alpha)$ time steps where $\alpha$ is $|\langle
t|s\rangle|$ and $B$ is a characteristic of the diffusion operator. Measuring
the w-state gives the target state with the success probability of $O(1/B^{2})$
and $O(B^{2})$ applications of the algorithm can boost it from $O(1/B^{2})$ to
$O(1)$, making the total time complexity $O(B^{3}/\alpha)$. In the special case
of Grover's algorithm, $D_{s}$ is $I_{s}$ and $B$ is very close to $1$. A more
efficient way to boost the success probability is quantum amplitude
amplification provided we can efficiently implement $I_{w}$. Such an efficient
implementation is not known so far. In this paper, we present an efficient
algorithm to approximate selective phase inversions of the unknown eigenstates
of an operator using phase estimation algorithm. This algorithm is used to
efficiently approximate $I_{w}$ which reduces the time complexity of general
algorithm to $O(B/\alpha)$. Though $O(B/\alpha)$ algorithms are known to exist,
our algorithm offers physical implementation advantages.
