Grover search

Suppose $N=2^n$ and $x$ is a nonzero $N$-bit string. Denote $t=|\{j:x_j=1\}|$. Given access to an $n$-qubit oracle $U_x$ such that $U_x\ket{j}=(-1)^{x_j}\ket{j}$, there exists a quantum algorithm that returns an index $j$ satisfying $x_j=1$ with probability $\sin^2((2k+1)\arcsin\sqrt{t/N})$, using $k$ queries to $U_x$ and $\mathcal{O}(kn)$ elementary gates.