Cited by 345Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyComplexity and Algorithms in Graphs

Quantum algorithms for algebraic problems

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Childs, Andrew M., van Dam, Wim·2010·Reviews of Modern Physics

Abstract

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation and, in particular, on problems with an algebraic flavor.

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Crossref · 10.1103/revmodphys.82.1

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264 of 264 references verified0 citation errors · 0 not checkable

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  • The sequences of operations yielded from phase estimation are often too deep to be feasible on today's NISQ devices.

    “However, an important technical point is that the sequences of operations (or quantum circuits, see Section 4.1.3) yielded from phase estimation are often too deep to be feasible on today's NISQ devices 51 .”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [51]

  • Early devices, also called 'pre-threshold' or NISQ devices, cannot support quantum error correction schemes, which require additional overhead.

    “Furthermore, these early devices, also called 'pre-threshold' or NISQ 51 devices, cannot support quantum error correction schemes, which require additional overhead.”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [51]

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Authors
Childs, A. M., & van Dam, W.
Affiliations
University of Waterloo (CA)
Venue
Reviews of Modern Physics
Published
2010-01-15
Volume
82
Issue
1
Pages
1-52
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
OpenAlex
W1972883454
Cited by
344
References
266
Citations by year
2026: 14 · 2025: 20 · 2024: 23 · 2023: 53 · 2022: 23 · 2021: 13 · 2020: 18 · 2019: 16 · 2018: 19 · 2017: 17 · 2016: 15 · 2015: 16 · 2014: 24 · 2013: 24 · 2012: 22
FWCI
23.31
Type
journal article
Language
en
Open access
Locations
  • Reviews of Modern Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
Keywords
quantum algorithms, algebraic problems, integer factorization, Shor's algorithm, quantum computing

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