Quantum Algorithms: A Survey of Applications and End-to-end Complexities

Alexander M. Dalzell; Sam McArdle; Mario Berta; Przemyslaw Bienias; Chi-Fang Chen; András Gilyén; Connor T. Hann; Michael J. Kastoryano; Emil T. Khabiboulline; Aleksander Kubica; Grant Salton; Samson Wang; Fernando G. S. L. Brandão

doi:10.1017/9781009639651

Quantum Algorithms

A Survey of Applications and End-to-end Complexities

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Costa, Pedro C. S. Morales, Mauro E. S. An, Dong and Sanders, Yuval R. 2025. Assessing quantum and classical approaches to combinatorial optimization: Testing quadratic speed-ups for heuristic algorithms. Physical Review A, Vol. 112, Issue. 2,

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Alexander M. Dalzell, AWS Center for Quantum Computing, Sam McArdle, AWS Center for Quantum Computing, Mario Berta, RWTH Aachen University, Przemyslaw Bienias, AWS Center for Quantum Computing, Chi-Fang Chen, University of California, Berkeley, András Gilyén, HUN-REN Alfréd Rényi Institute of Mathematics, Connor T. Hann, AWS Center for Quantum Computing, Michael J. Kastoryano, University of Copenhagen, Emil T. Khabiboulline, National Institute of Standards and Technology, Aleksander Kubica, Yale University, Grant Salton, Amazon Quantum Solutions Lab, Samson Wang, Caltech, Fernando G. S. L. Brandão, AWS Center for Quantum Computing

Publisher:: Cambridge University Press
Online publication date:: May 2025
Print publication year:: 2025
Online ISBN:: 9781009639651
DOI:: https://doi.org/10.1017/9781009639651
Creative Commons:: 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/creativelicenses

Subjects:: Algorithmics, Complexity, Computer Algebra, Computational Geometry, Physics and Astronomy, Computer Science, Quantum Physics, Quantum Information and Quantum Computation

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The 1994 discovery of Shor's quantum algorithm for integer factorization—an important practical problem in the area of cryptography—demonstrated quantum computing's potential for real-world impact. Since then, researchers have worked intensively to expand the list of practical problems that quantum algorithms can solve effectively. This book surveys the fruits of this effort, covering proposed quantum algorithms for concrete problems in many application areas, including quantum chemistry, optimization, finance, and machine learning. For each quantum algorithm considered, the book clearly states the problem being solved and the full computational complexity of the procedure, making sure to account for the contribution from all the underlying primitive ingredients. Separately, the book provides a detailed, independent summary of the most common algorithmic primitives. It has a modular, encyclopedic format to facilitate navigation of the material and to provide a quick reference for designers of quantum algorithms and quantum computing researchers.

‘This timely and forward-looking survey captures the state-of-the-art in quantum computing. Focusing on cutting-edge applications and recent advances in quantum primitives, it serves as an essential resource for understanding the rapidly evolving role of quantum algorithms in scientific discovery.’

Lin Lin - University of California, Berkeley

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