Amplitude estimation via maximum likelihood on noisy quantum computer

Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude a given state, which is core sub- routine various computing tasks such as Monte Carlo methods. One those based on maximum likelihood estimate with parallelized circuits. In this paper, extend method so it incorporates realistic noise effect, and then give an experimental demonstration superconducting IBM Quantum device. The estimator constructed model assuming depolarization noise. We formulate problem two-parameters estimation respect to target parameter parameter. particular show there exist anomalous values, where Fisher information matrix becomes degenerate consequently error cannot improved even by increasing number amplifications. shows proposed achieves speedup queries, though saturates due This saturated value consistent theory, implies validity thereby enables us predict basic requirement hardware components (particularly gate error) computers realize task.