  In this paper, we propose a quantum amplitude estimation method that uses a
modified Grover operator and quadratically improves the estimation accuracy in
the ideal case, as in the conventional one using the standard Grover operator.
Under the depolarizing noise, the proposed method can outperform the
conventional one in the sense that it can in principle achieve the ultimate
estimation accuracy characterized by the quantum Fisher information in the
limit of a large number of qubits, while the conventional one cannot achieve
the same value of ultimate accuracy. In general this superiority requires a
sophisticated adaptive measurement, but we numerically demonstrate that the
proposed method can outperform the conventional one and approach to the
ultimate accuracy, even with a simple non-adaptive measurement strategy.
