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10 - Quantum linear algebra

from Part II - Quantum algorithmic primitives

Published online by Cambridge University Press:  03 May 2025

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
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Summary

This chapter covers quantum algorithmic primitives related to linear algebra. We discuss block-encodings, a versatile and abstract access model that features in many quantum algorithms. We explain how block-encodings can be manipulated, for example by taking products or linear combinations. We discuss the techniques of quantum signal processing, qubitization, and quantum singular value transformation, which unify many quantum algorithms into a common framework.

Keywords

block-encodinglinear algebraquantum signal processingqubitizationquantum singular value transformationlinear combination of unitariesquantum algorithmic primitivequantum algorithm
Type
Chapter
Information
Quantum Algorithms
A Survey of Applications and End-to-end Complexities
 , pp. 188 - 209
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/

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