  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 the
variants and the original algorithm is that the variants do not need quantum
phase estimation (QPE), a key component of the canonical QAE (Brassard et al.,
2002), that is composed of many expensive operations on NISQ devices. In this
paper, 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. The
comparisons are drawn based on number of oracle queries, quantum circuit depth,
and other complexities of implementation for a fixed accuracy. We discuss the
strengths and limitations of each algorithm from a computational perspective.
