  Many quantum algorithms contain an important subroutine, the quantum
amplitude estimation. As the name implies, this is essentially the parameter
estimation problem and thus can be handled via the established statistical
estimation theory. However, this problem has an intrinsic difficulty that the
system, i.e., the real quantum computing device, inevitably introduces unknown
noise; the probability distribution model then has to incorporate many nuisance
noise parameters, resulting that the construction of an optimal estimator
becomes inefficient and difficult. For this problem, we apply the theory of
nuisance parameters (more specifically, the parameter orthogonalization method)
to precisely compute the maximum likelihood estimator for only the target
amplitude parameter, by removing the other nuisance noise parameters. That is,
we can estimate the amplitude parameter without estimating the noise
parameters. We validate the parameter orthogonalization method in a numerical
simulation and study the performance of the estimator in the experiment using a
real superconducting quantum device.

Quantum Physics