  Quantum amplitude estimation (QAE) is a pivotal quantum algorithm to estimate
the squared amplitude $a$ of the target basis state in a quantum state
$|\Phi\rangle$. Various improvements on the original quantum phase
estimation-based QAE have been proposed for resource reduction. One of such
improved versions is iterative quantum amplitude estimation (IQAE), which
outputs an estimate $\hat{a}$ of $a$ through the iterated rounds of the
measurements on the quantum states like $G^k|\Phi\rangle$, with the number $k$
of operations of the Grover operator $G$ (the Grover number) and the shot
number determined adaptively. This paper investigates the bias in IQAE. Through
the numerical experiments to simulate IQAE, we reveal that the estimate by IQAE
is biased and the bias is enhanced for some specific values of $a$. We see that
the termination criterion in IQAE that the estimated accuracy of $\hat{a}$
falls below the threshold is a source of the bias. Besides, we observe that
$k_\mathrm{fin}$, the Grover number in the final round, and $f_\mathrm{fin}$, a
quantity affecting the probability distribution of measurement outcomes in the
final round, are the key factors to determine the bias, and the bias
enhancement for specific values of $a$ is due to the skewed distribution of
$(k_\mathrm{fin},f_\mathrm{fin})$. We also present a bias mitigation method:
just re-executing the final round with the Grover number and the shot number
fixed.
