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 of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits; in this paper, we extend this method so that it can deal with the realistic noise effect. The validity of the proposed noise model is supported by an experimental demonstration on an IBM Q device, which accordingly enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.