The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Prediction by linear regression on a quantum computer
Open accessAbstract
We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least-squares optimization. In contrast to related previous contributions suffering from the problem of reading out the optimal parameters of the fit, our scheme focuses on the machine-learning task of guessing the output corresponding to a new input given examples of data points. Furthermore, we adapt the algorithm to process nonsparse data matrices that can be represented by low-rank approximations, and significantly improve the dependency on its condition number. The prediction result can be accessed through a single-qubit measurement or used for further quantum information processing routines. The algorithm's runtime is logarithmic in the dimension of the input space provided the data is given as quantum information as an input to the routine.
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Citations
Cites
Quantum Algorithm for Linear Systems of Equations
Harrow, A. W., Hassidim, A., & Lloyd, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.150502 · Cited by 3,325
Trefethen, L. N., & Bau, III (1997) · doi:10.1137/1.9780898719574 · Cited by 3,301
Singular value decomposition and least squares solutions
Golub, G. H., & Reinsch, C. (1970) · Numerische Mathematik · doi:10.1007/bf02163027 · Cited by 2,929 · cited 1×
“…matrix containing all training inputs as rows) and the target vector y = ( y (1) , ..., y ( M ) ) T , the least squares error becomes | Xw − y | 2 , and it is a widely used result [16] that the solution to the least squares problem is given by where X + is the Moore-Penrose pseudoinverse of X .”
BackgroundQuantum Support Vector Machine for Big Data Classification
Rebentrost, P., Mohseni, M., & Lloyd, S. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.130503 · Cited by 1,951
Computational Complexity: A Modern Approach
Arora, S., & Barak, B. (2009) · doi:10.1017/cbo9780511804090 · Cited by 1,690
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385
Giovannetti, V., Lloyd, S., & Maccone, L. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.160501 · Cited by 935
Aaronson, S. (2015) · Nature Physics · doi:10.1038/nphys3272 · Cited by 567
Quantum Algorithm for Data Fitting
Wiebe, N., Braun, D., & Lloyd, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.050505 · Cited by 528
Preconditioned Quantum Linear System Algorithm
Clader, B. D., Jacobs, B. C., & Sprouse, C. R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.250504 · Cited by 288
Cited by
Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., & Lloyd, S. (2017) · Nature · doi:10.1038/nature23474 · Cited by 4,779
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 2,231
Quantum Machine Learning in Feature Hilbert Spaces
Schuld, M., & Killoran, N. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.040504 · Cited by 1,840
Self-citationMitarai, K., Negoro, M., Kitagawa, M., & Fujii, K. (2018) · Physical Review A · doi:10.1103/physreva.98.032309 · Cited by 1,639
Quantum computing for finance: Overview and prospects
Orús, R., Mugel, S., & Lizaso, E. (2019) · Reviews in Physics · doi:10.1016/j.revip.2019.100028 · Cited by 668
Metadata
- Authors
- Schuld, M., Sinayskiy, I., & Petruccione, F.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2016-08-30
- Volume
- 94
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2489886790
- Cited by
- 274
- References
- 10
- FWCI
- 17.15
- Type
- journal article
- Language
- en
- Open access
- green
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