  Quantum Amplitude Estimation (QAE) -- a technique by which the amplitude of a
given quantum state can be estimated with quadratically fewer queries than by
standard sampling -- is a key sub-routine in several important quantum
algorithms, including Grover search and Quantum Monte-Carlo methods. An
obstacle to implementing QAE in near-term noisy intermediate-scale quantum
(NISQ) devices has been the need to perform Quantum Phase Estimation (QPE) -- a
costly procedure -- as a sub-routine. This impediment was lifted with various
QPE-free methods of QAE, wherein Grover queries of varying depths / powers
(often according to a "schedule") are followed immediately by measurements and
classical post-processing techniques like maximum likelihood estimation (MLE).
Existing analyses as to the optimality of various query schedules in these
QPE-free QAE schemes have hitherto assumed noise-free systems. In this work, we
analyse QPE-free QAE under common noise models that may afflict NISQ devices
and report on the optimality of various query schedules in the noisy regime. We
demonstrate that, given an accurate noise characterization of one's system, one
must choose a schedule that balances the trade-off between the greater ideal
performance achieved by higher-depth circuits, and the correspondingly greater
accumulation of noise-induced error.
