On the bias in iterative quantum amplitude estimation

Miyamoto, Koichi

EPJ Quantum Technology, 2024, 11(1), 42

Number of Access:135（2025-08-15 10:59 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/97840

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Title
On the bias in iterative quantum amplitude estimation
Creator
NRID
1000090936270 1000090936270
ORCID
0000-0003-2478-0841 0000-0003-2478-0841
researchmap permalink
koichimiyamoto koichimiyamoto
Scopus Author ID
57219247023 57219247023
CreatorName
Miyamoto, Koichi
Subject
Quantum algorithm
Quantum amplitude estimation
Statistical bias
Description
Miyamoto K. On the bias in iterative quantum amplitude estimation. EPJ Quantum Technology 11, 42 (2024); https://doi.org/10.1140/epjqt/s40507-024-00253-x.
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 |Φ〉. 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 Gk|Φ〉, 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 kfin, the Grover number in the final round, and ffin, 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 (kfin,ffin). We also present a bias mitigation method: just re-executing the final round with the Grover number and the shot number fixed.
Publisher
Springer Science and Business Media Deutschland GmbH
Source Title
EPJ Quantum Technology
Volume (Issue)
11(1)
Page
42
Date of Issued
2024-06-25
Language
English
Handle URL
https://hdl.handle.net/11094/97840
eISSN
21960763
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.1140/epjqt/s40507-024-00253-x
Access Rights
open access
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This article is licensed under a Creative Commons Attribution 4.0 International License.
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Category
学術雑誌論文 Journal Article