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arXiv · 2306.16695

Asymptotically Optimal Quantum Amplitude Estimation by Generalized Qubitization

Xi Lu·Hongwei Lin
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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.

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Xi Lu, Hongwei Lin. 2023-06-29. Asymptotically Optimal Quantum Amplitude Estimation by Generalized Qubitization. https://arxiv.org/abs/2306.16695

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