  In quantum computation, amplitude estimation is a fundamental subroutine that
is utilized in various quantum algorithms. A general important task of such
estimation problems is to characterize the estimation lower bound, which is
referred to as quantum Cram\'er-Rao bound (QCRB), and to construct an optimal
estimator that achieves QCRB. This paper studies the amplitude estimation in
the presence of depolarizing noise with unknown intensity. The main difficulty
in this problem is that the optimal measurement depends on both the unknown
quantum state and the amplitude we aim to estimate. To deal with these issues,
we utilize the variational quantum circuits to approximate the (unknown)
optimal measurement basis combined with the 2-step adaptive estimation strategy
which was proposed in the quantum estimation theory.We numerically show that
the proposed method can nearly attain the QCRB.
