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5 - Continuous optimization

from Part I - Areas of application

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 applications of quantum computing in the area of continuous optimization, including both convex and nonconvex optimization. We discuss quantum algorithms for computing Nash equilibria for zero-sum games and for solving linear, second-order, and semidefinite programs. These algorithms are based on quantum implementations of the multiplicative weights update method or interior point methods. We also discuss general quantum algorithms for convex optimization which can provide a speedup in cases where the objective function is much easier to evaluate than the gradient of the objective function. Finally, we cover quantum algorithms for escaping saddle points and finding local minima in nonconvex optimization problems.

Keywords

optimizationconvex optimizationnonconvex optimizationzero-sum gameslinear programsemidefinite programmultiplicative weightsinterior point methods
Type
Chapter
Information
Quantum Algorithms
A Survey of Applications and End-to-end Complexities
 , pp. 78 - 97
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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