Comparison of Amplitude Estimation Algorithms by Implementation

TL;DR

This paper compares recent quantum amplitude estimation algorithms by implementing them on Qiskit, analyzing their efficiency and complexity in terms of oracle queries and circuit depth for fixed accuracy.

Contribution

It provides a practical implementation and comparative analysis of two modern QAE algorithms, highlighting their strengths and limitations on NISQ devices.

Findings

Suzuki et al. algorithm requires fewer oracle queries.

Grinko et al. algorithm has shallower quantum circuits.

Both algorithms show trade-offs between complexity and accuracy.

Abstract

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.