  In this paper, we introduce an efficient algorithm for the quantum amplitude
estimation task which works in noisy intermediate-scale quantum(NISQ) devices.
The quantum amplitude estimation is an important problem which has various
applications in fields such as quantum chemistry, machine learning, and
finance. Because the well-known algorithm for the quantum amplitude estimation
using the phase estimation cannot be executed in NISQ devices, alternative
approaches have been proposed in recent literature. Some of them provide a
proof of the upper bound which almost achieves the Heisenberg scaling. However,
the constant factor is large and thus the bound is loose. Our contribution in
this paper is to provide the algorithm such that the upper bound of query
complexity almost achieves the Heisenberg scaling and the constant factor is
small.
