On the bias in iterative quantum amplitude estimation

IF 5.8 2区 物理与天体物理 Q1 OPTICS
Koichi Miyamoto
{"title":"On the bias in iterative quantum amplitude estimation","authors":"Koichi Miyamoto","doi":"10.1140/epjqt/s40507-024-00253-x","DOIUrl":null,"url":null,"abstract":"<div><p>Quantum amplitude estimation (QAE) is a pivotal quantum algorithm to estimate the squared amplitude <i>a</i> of the target basis state in a quantum state <span>\\(|{\\Phi}\\rangle \\)</span>. Various improvements on the original quantum phase estimation-based QAE have been proposed for resource reduction. One of such improved versions is iterative quantum amplitude estimation (IQAE), which outputs an estimate <i>â</i> of <i>a</i> through the iterated rounds of the measurements on the quantum states like <span>\\(G^{k}|{\\Phi}\\rangle \\)</span>, with the number <i>k</i> of operations of the Grover operator <i>G</i> (the Grover number) and the shot number determined adaptively. This paper investigates the bias in IQAE. Through the numerical experiments to simulate IQAE, we reveal that the estimate by IQAE is biased and the bias is enhanced for some specific values of <i>a</i>. We see that the termination criterion in IQAE that the estimated accuracy of <i>â</i> falls below the threshold is a source of the bias. Besides, we observe that <span>\\(k_{\\mathrm{fin}}\\)</span>, the Grover number in the final round, and <span>\\(f_{\\mathrm{fin}}\\)</span>, a quantity affecting the probability distribution of measurement outcomes in the final round, are the key factors to determine the bias, and the bias enhancement for specific values of <i>a</i> is due to the skewed distribution of <span>\\((k_{\\mathrm{fin}},f_{\\mathrm{fin}})\\)</span>. We also present a bias mitigation method: just re-executing the final round with the Grover number and the shot number fixed.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":null,"pages":null},"PeriodicalIF":5.8000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-024-00253-x","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-024-00253-x","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0

Abstract

Quantum amplitude estimation (QAE) is a pivotal quantum algorithm to estimate the squared amplitude a of the target basis state in a quantum state \(|{\Phi}\rangle \). Various improvements on the original quantum phase estimation-based QAE have been proposed for resource reduction. One of such improved versions is iterative quantum amplitude estimation (IQAE), which outputs an estimate â of a through the iterated rounds of the measurements on the quantum states like \(G^{k}|{\Phi}\rangle \), with the number k of operations of the Grover operator G (the Grover number) and the shot number determined adaptively. This paper investigates the bias in IQAE. Through the numerical experiments to simulate IQAE, we reveal that the estimate by IQAE is biased and the bias is enhanced for some specific values of a. We see that the termination criterion in IQAE that the estimated accuracy of â falls below the threshold is a source of the bias. Besides, we observe that \(k_{\mathrm{fin}}\), the Grover number in the final round, and \(f_{\mathrm{fin}}\), a quantity affecting the probability distribution of measurement outcomes in the final round, are the key factors to determine the bias, and the bias enhancement for specific values of a is due to the skewed distribution of \((k_{\mathrm{fin}},f_{\mathrm{fin}})\). We also present a bias mitigation method: just re-executing the final round with the Grover number and the shot number fixed.

关于迭代量子振幅估计中的偏差
量子振幅估计(QAE)是一种关键的量子算法,用于估计量子态(|{\Phi}\rangle \)中目标基态的振幅平方 a。为了减少资源,人们对原始的基于量子相位估计的 QAE 提出了各种改进方案。其中一个改进版本是迭代量子振幅估计(IQAE),它通过对量子态的迭代轮测量输出一个估计值â,如\(G^{k}|{\Phi}\rangle \),格罗弗算子 G 的运算次数 k(格罗弗数)和射击数是自适应确定的。本文研究了 IQAE 中的偏差。通过模拟 IQAE 的数值实验,我们发现 IQAE 的估计值是有偏差的,并且在某些特定的 a 值下偏差会增强。此外,我们还发现最后一轮的格罗弗数\(k_{/mathrm{fin}}\)和影响最后一轮测量结果概率分布的量\(f_{/mathrm{fin}}\)是决定偏差的关键因素,而特定 a 值的偏差增强是由于\((k_{/mathrm{fin}},f_{/mathrm{fin}})\)的倾斜分布造成的。我们还提出了一种减轻偏差的方法:只需在固定格罗弗数和射击数的情况下重新执行最后一轮。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
EPJ Quantum Technology
EPJ Quantum Technology Physics and Astronomy-Atomic and Molecular Physics, and Optics
CiteScore
7.70
自引率
7.50%
发文量
28
审稿时长
71 days
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following: Quantum measurement, metrology and lithography Quantum complex systems, networks and cellular automata Quantum electromechanical systems Quantum optomechanical systems Quantum machines, engineering and nanorobotics Quantum control theory Quantum information, communication and computation Quantum thermodynamics Quantum metamaterials The effect of Casimir forces on micro- and nano-electromechanical systems Quantum biology Quantum sensing Hybrid quantum systems Quantum simulations.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信