Quantum algorithms for algebraic problems
Open accessAbstract
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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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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A Comprehensive Survey on Quantum Machine Learning and Possible Applications
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- Authors
- Childs, A. M., & van Dam, W.
- Affiliations
- University of Waterloo (CA)
- ORCID
- Childs, Andrew M.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- 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
- green
- arxiv.org
- 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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