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Quantum Support Vector Machine for Big Data Classification
Open accessAbstract
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.
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In the citing paper
“Exponential speedup has, for instance, shown to be possible for quantum support vector machines [110]”
From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [110]
In the citing paper
“First, by more sophisticated Trotter-Suzuki decompositions 261 , the approximation error can be made to depend on progressively-higher orders in τ 196,260,261 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [261]
In the citing paper
“If |χ is some other vector, then the method provides a method for supervised learning and cluster assignment 9,10,21,28 :”
From Quantum principal component analysis (2014) · cites this paper as [28]
In the citing paper
“Note that this expressivity boost is not limited to neural networks and has been observed, for instance, for support vector machines.[222,228,229]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [222]
In the citing paper
“The first advantage has been leveraged in deriving the quantum realization of the principal components analysis algorithm [221] and of a support vector machine.[222]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [222]
In the citing paper
“Rebentrost et al. [75] presented a quantum algorithm that can train a SVM with a polynomial kernel in O log N ð Þ, and this was later extended to the radial basis function (RBF) kernel [76].”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [75]
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Metadata
- Authors
- Rebentrost, P., Mohseni, M., & Lloyd, S.
- Affiliations
- Massachusetts Institute of Technology (US)
- Google (United States) (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2014-09-25
- Volume
- 113
- Issue
- 13
- Pages
- 130503-130503
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2103956991
- Cited by
- 1,951
- References
- 30
- Citations by year
- 2026: 229 · 2025: 306 · 2024: 274 · 2023: 277 · 2022: 205 · 2021: 208 · 2020: 151 · 2019: 105 · 2018: 77 · 2017: 54 · 2016: 45 · 2015: 13 · 2014: 7
- FWCI
- 39.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- arXiv (Cornell University)
- Funders
- Defense Advanced Research Projects Agency (DARPA)
- National Science Foundation (NSF)
- Eni
- Air Force Office of Scientific Research (AFOSR)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum support vector machine, quantum machine learning, big data classification, binary classification, quantum advantage, matrix inversion, kernel matrix, quantum computing
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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