Guest Column: A Survey of Quantum Learning Theory
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This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.
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Save for idealized examples, quantum computers can learn no more information than a classical computer from the same training set.
“Save for idealized examples, quantum computers can learn no more information than a classical computer from the same training set [64].”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [64]
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References 90 · Cited by 152
Research works printed but not linked: 7
- S. Aaronson. The learnability of quantum states. Proceedings of the Royal Society of London, 463(2088), 2007. quant-ph/0608142. · arXiv
- A. S. Holevo. Bounds for the quantity of information transmitted by a quantum commu- nication channel. Problemy Peredachi Informatsii, 9(3):3-11, 1973. English translation in Problems of Information Transmission, 9:177-183, 1973.
- R. Kothari. An optimal quantum algorithm for the oracle identification problem. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014), pages 482-493, 2014. arXiv:1311.7685. · arXiv
- A. Klivans and R. Servedio. Learning DNF in time 2 Õ(n 1/3 ) . Journal of Computer and System Sciences, 68(2):303-318, 2004. Earlier version in STOC'01.
- C. Y.-Y. Lin and H. Lin. Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester. Theory of Computing, 12:1-35, 2016. Earlier version in CCC'15. arXiv:1410.0932. · arXiv
- Y. Manin. Vychislimoe i nevychislimoe (computable and noncomputable). Soviet Radio, pages 13-15, 1980. In Russian.
- M. Talagrand. Sharper bounds for Gaussian and empirical processes. The Annals of Probability, pages 28-76, 1994.
- Authors
- Arunachalam, S., & de Wolf, R.
- Affiliations
- Centrum Wiskunde & Informatica (NL)
- CWI and University of Amsterdam, The Netherlands
- Venue
- ACM SIGACT News
- Published
- 2017-06-12
- Volume
- 48
- Issue
- 2
- Pages
- 41-67
- ISSN
- 0163-5700 (ISSN-L)
- OpenAlex
- W2580838454
- Cited by
- 152
- References
- 90
- Citations by year
- 2026: 14 · 2025: 17 · 2024: 14 · 2023: 26 · 2022: 14 · 2021: 32 · 2020: 20 · 2019: 10 · 2018: 5
- FWCI
- 5.71
- Type
- journal article
- Language
- en
- Open access
- green
- ir.cwi.nl
- Locations
- ACM SIGACT News (publishedVersion)
- Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands (submittedVersion)
- UvA-DARE (University of Amsterdam) (submittedVersion, other-oa)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- Data Archiving and Networked Services (DANS) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum computing hardware, exact learning, membership queries, PAC learning, agnostic learning, computational learning theory, quantum machine learning
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