  We put forward a Quantum Amplitude Estimation algorithm delivering superior
performance (lower quantum computational complexity and faster classical
computation parts) compared to the approaches available to-date. The algorithm
does not relay on the Quantum Fourier Transform and its quantum computational
complexity is of order $O(\frac{1}{\varepsilon})$ in terms of the target
accuracy $\varepsilon>0$. The $O(\frac{1}{\varepsilon})$ bound on quantum
computational complexity is also superior compared to those in the earlier
approaches due to smaller constants. Moreover, a much tighter bound is obtained
by means of computer-assisted estimates for the expected value of quantum
computational complexity. The correctness of the algorithm and the
$O(\frac{1}{\varepsilon})$ bound on quantum computational complexity are
supported by precise proofs.
