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Since the quantum amplitude estimation (QAE) was invented by Brassard et al.,2002, several advanced algorithms have recently been published (Grinko et al.,2019, Aaronson et al, and Suzuki et al., 2020). The main difference between thevariants and the original algorithm is that the variants do not need quantumphase estimation (QPE), a key component of the canonical QAE (Brassard et al.,2002), that is composed of many expensive operations on NISQ devices. In thispaper, we compare and analyze two of these new QAE approaches (Grinko et al.,2019, and Suzuki et al., 2020) by implementation using the Qiskit package. Thecomparisons are drawn based on number of oracle queries, quantum circuit depth,and other complexities of implementation for a fixed accuracy. We discuss thestrengths and limitations of each algorithm from a computational perspective.

Comparison of Amplitude Estimation Algorithms by Implementation