Automation of the Quantum Algorithm HHL for implementing two-dimensional SVMs
Resumo
Support Vector Machine (SVM) is considered one of the main classification Machine Learning algorithms. Following the original formulation,an SVM generation has quadratic complexity, leaving room for exploring resolution methods with better performance. One way to enhance its efficiency is by utilizing Quantum Computing algorithms, such as the HHL. This work presents an automation of a Quantum Machine Learning algorithm that uses HHL to generate SVMs fixed at the origin of a two-dimensional hyperplane.Referências
A. Adedoyin et al. (2018). Quantum algorithm implementations for beginners. arXiv preprint arXiv:1804.03719.
X.-D. Cai et al. (2013). Experimental quantum computing to solve systems of linear equations. Physical Review Letters, 110(23):230501.
J. Cervantes et al. (2020). A comprehensive survey on support vector machine classification: Applications, challenges and trends. Neurocomputing, 408:189–215.
C. Cortes and V. Vapnik (1995). Support-vector networks. Machine learning, 20:273–297.
A. Cross (2018). The ibm q experience and qiskit open-source quantum computing software. In APS March meeting abstracts, volume 2018, pages L58–003.
B. Duan et al. (2020). A survey on HHL algorithm: From theory to application in quantum machine learning. Physics Letters A, 384(24):126595.
L. Gyongyosi and S. Imre (2019). A survey on quantum computing technology. Computer Science Review, 31:51–71.
A. W. Harrow, A. Hassidim, and S. Lloyd (2009). Quantum algorithm for linear systems of equations. Physical Review Letters, 103(15):150502.
C. B.-S. . v. W. C. Larhmam (2018). Maximum-margin hyperplane and margin for an SVM trained on two classes. samples on margins are called support vectors. [link].
H. J. Morrell Jr, A. Zaman, and H. Y. Wong (2021). Step-by-step hhl algorithm walk-through to enhance the understanding of critical quantum computing concepts. arXiv preprint arXiv:2108.09004.
M. A. Nielsen and I. L. Chuang (2010). Quantum computation and quantum information. Cambridge University Press.
E. Pednault et al. (2017). Pareto-efficient quantum circuit simulation using tensor contraction deferral. arXiv preprint arXiv:1710.05867.
P. Rebentrost, M. Mohseni, and S. Lloyd (2014). Quantum support vector machine for big data classification. Physical Review Letters, 113(13):130503.
W. N. Street, W. H. Wolberg, and O. L. Mangasarian (1993). Nuclear feature extraction for breast tumor diagnosis. In Biomedical image processing and biomedical visualization, volume 1905, pages 861–870. SPIE.
J. A. Suykens and J. Vandewalle (1999). Least squares support vector machine classifiers. Neural processing letters, 9:293–300.
J. Yang, A. J. Awan, and G. Vall-Llosera (2019). Support vector machines on noisy intermediate scale quantum computers. arXiv preprint arXiv:1909.11988.
X.-D. Cai et al. (2013). Experimental quantum computing to solve systems of linear equations. Physical Review Letters, 110(23):230501.
J. Cervantes et al. (2020). A comprehensive survey on support vector machine classification: Applications, challenges and trends. Neurocomputing, 408:189–215.
C. Cortes and V. Vapnik (1995). Support-vector networks. Machine learning, 20:273–297.
A. Cross (2018). The ibm q experience and qiskit open-source quantum computing software. In APS March meeting abstracts, volume 2018, pages L58–003.
B. Duan et al. (2020). A survey on HHL algorithm: From theory to application in quantum machine learning. Physics Letters A, 384(24):126595.
L. Gyongyosi and S. Imre (2019). A survey on quantum computing technology. Computer Science Review, 31:51–71.
A. W. Harrow, A. Hassidim, and S. Lloyd (2009). Quantum algorithm for linear systems of equations. Physical Review Letters, 103(15):150502.
C. B.-S. . v. W. C. Larhmam (2018). Maximum-margin hyperplane and margin for an SVM trained on two classes. samples on margins are called support vectors. [link].
H. J. Morrell Jr, A. Zaman, and H. Y. Wong (2021). Step-by-step hhl algorithm walk-through to enhance the understanding of critical quantum computing concepts. arXiv preprint arXiv:2108.09004.
M. A. Nielsen and I. L. Chuang (2010). Quantum computation and quantum information. Cambridge University Press.
E. Pednault et al. (2017). Pareto-efficient quantum circuit simulation using tensor contraction deferral. arXiv preprint arXiv:1710.05867.
P. Rebentrost, M. Mohseni, and S. Lloyd (2014). Quantum support vector machine for big data classification. Physical Review Letters, 113(13):130503.
W. N. Street, W. H. Wolberg, and O. L. Mangasarian (1993). Nuclear feature extraction for breast tumor diagnosis. In Biomedical image processing and biomedical visualization, volume 1905, pages 861–870. SPIE.
J. A. Suykens and J. Vandewalle (1999). Least squares support vector machine classifiers. Neural processing letters, 9:293–300.
J. Yang, A. J. Awan, and G. Vall-Llosera (2019). Support vector machines on noisy intermediate scale quantum computers. arXiv preprint arXiv:1909.11988.
Publicado
20/05/2024
Como Citar
PINHEIRO, Gabriela; KOWADA, Luis Antonio Brasil.
Automation of the Quantum Algorithm HHL for implementing two-dimensional SVMs. In: WORKSHOP DE REDES QUÂNTICAS, 1. , 2024, Niterói/RJ.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2024
.
p. 13-18.
DOI: https://doi.org/10.5753/wqunets.2024.2861.
