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22 - Quantum interior point methods

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 interior point methods, which are quantum algorithmic primitives for application to convex optimization problems, particularly linear, second-order, and semidefinite programs. Interior point methods are a successful classical iterative technique that solve a linear system of equations at each iteration. Quantum interior point methods replace this step with quantum a quantum linear system solver combined with quantum tomography, potentially offering a polynomial speedup.

Keywords

optimizationconvex optimizationinterior point methodslinear programsemidefinite programquantum algorithmquantum algorithmic primitive
Type
Chapter
Information
Quantum Algorithms
A Survey of Applications and End-to-end Complexities
 , pp. 291 - 298
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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