Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-669899f699-tpknm Total loading time: 0 Render date: 2025-05-04T02:34:17.146Z Has data issue: false hasContentIssue false

14 - Amplitude amplification and estimation

from Part II - Quantum algorithmic primitives

Published online by Cambridge University Press:  aN Invalid Date NaN

Alexander M. Dalzell ,
Sam McArdle ,
Mario Berta ,
Przemyslaw Bienias ,
Chi-Fang Chen ,
András Gilyén ,
Connor T. Hann ,
Michael J. Kastoryano ,
Emil T. Khabiboulline  and
Aleksander Kubica
...Show all authors
Alexander M. Dalzell
Affiliation:
AWS Center for Quantum Computing
Sam McArdle
Affiliation:
AWS Center for Quantum Computing
Mario Berta
Affiliation:
RWTH Aachen University
Przemyslaw Bienias
Affiliation:
AWS Center for Quantum Computing
Chi-Fang Chen
Affiliation:
University of California, Berkeley
András Gilyén
Affiliation:
HUN-REN Alfréd Rényi Institute of Mathematics
Connor T. Hann
Affiliation:
AWS Center for Quantum Computing
Michael J. Kastoryano
Affiliation:
University of Copenhagen
Emil T. Khabiboulline
Affiliation:
National Institute of Standards and Technology
Aleksander Kubica
Affiliation:
Yale University
Grant Salton
Affiliation:
Amazon Quantum Solutions Lab
Samson Wang
Affiliation:
Caltech
Fernando G. S. L. Brandão
Affiliation:
AWS Center for Quantum Computing
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Summary

This chapter covers the quantum algorithmic primitives of amplitude amplification and amplitude estimation. Amplitude amplification is a generalization of Grover’s quantum algorithm for the unstructured search problem. Amplitude estimation can be understood in a similar framework, where it utilizes quantum phase estimation to estimate the value of the amplitude or probability associated with a quantum state. Both amplitude amplification and amplitude estimation provide a quadratic speedup over their classical counterparts, and feature prominently as an ingredient in many end-to-end algorithms.

Keywords

Grover’s search algorithmamplitude amplificationamplitude estimationquantum Fourier transformquantum phase estimationquantum algorithmquantum algorithmic primitive
Type
Chapter
Information
Quantum Algorithms
A Survey of Applications and End-to-end Complexities
 , pp. 235 - 242
Publisher: Cambridge University Press
Print publication year: 2025
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/cclicenses/

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×