Asymptotically Optimal Quantum Amplitude Estimation by Generalized Qubitization

TL;DR

This paper introduces a generalized qubitization method that achieves the optimal asymptotic accuracy in quantum amplitude estimation, improving the understanding of error bounds and query efficiency.

Contribution

It presents a novel generalized qubitization technique enabling simultaneous polynomial function encoding, leading to asymptotically optimal quantum amplitude estimation.

Findings

Error bound of approximately 1.28 L^{-1} for standard deviation in amplitude estimation

Generalized qubitization allows simultaneous polynomial encoding

Achieves tight asymptotic accuracy bound

Abstract

We first show that the standard deviation error of quantum amplitude estimation is asymptotically lower bounded by approximately $1.28 L^{-1}$, where $L$ is the number of queries. Then we propose a generalized qubitization that can block-encode several polynomial functions simultaneously, and show how it can help estimating quantum amplitude to achieve the optimal asymptotic accuracy, so the bound is tight.