publication . Article . Preprint . 2016

A Quantum Implementation Model for Artificial Neural Networks

Ammar DASKIN;
Open Access
  • Published: 19 Sep 2016 Journal: Quanta, volume 7, page 7 (eissn: 1314-7374, Copyright policy)
  • Publisher: Quanta
Abstract
<jats:p>The learning process for multilayered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow–Hoff formula, do not change the eigenvectors of the weight matrix while flatting the eigenvalues. In infinity, these iterative formulas result in terms formed by the principal components of the weight matrix, namely, the eigenvectors corresponding to the non-zero eigenvalues. In quantum computing, the phase estimation algorithm is known to provide speedups over the conventional algorithms for the eigenvalue-related problems. Combining the quantum amplitude amplificat...
Subjects
ACM Computing Classification System: MathematicsofComputing_NUMERICALANALYSIS
free text keywords: Quantum Physics, Computer Science - Learning, Computer Science - Neural and Evolutionary Computing, Science, Q
36 references, page 1 of 3

[1] S. S. Haykin, Neural networks and learning machines. Pearson Upper Saddle River, NJ, USA:, 2009, vol. 3.

[2] H. Abdi, “Linear algebra for neural networks,” International encyclopedia of the social and behavioral sciences. Elsevier, Oxford UK, 2001.

[3] H. Abdi, D. Valentin, B. Edelman, and A. J. O'Toole, “More about the difference between men and women: evidence from linear neural networks and the principal-component approach,” Perception, vol. 24, no. 5, pp. 539-562, 1995.

[4] B. Widrow, M. E. Hoff et al., “Adaptive switching circuits,” in IRE WESCON convention record, vol. 4, no. 1. New York, 1960, pp. 96- 104. [OpenAIRE]

[5] H. Abdi, D. Valentin, B. Edelman, and A. J. O'Toole, “A widrow-hoff learning rule for a generalization of the linear auto-associator,” Journal of Mathematical Psychology, vol. 40, no. 2, pp. 175-182, 1996.

[6] S. Lloyd, “Ultimate physical limits to computation,” Nature, vol. 406, no. 6799, pp. 1047-1054, 2000.

[7] R. Feynman, “Simulating physics with computers,” International Journal of Theoretical Physics, vol. 21, pp. 467-488, 1982, 10.1007/BF02650179.

[8] C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, “Strengths and weaknesses of quantum computing,” SIAM Journal on Compututing, vol. 26, no. 5, pp. 1510-1523, 1997.

[9] D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proceedings of the Royal Society of London A: Mathematical and Physical Sciences, vol. 400, no. 1818, pp. 97-117, 1985.

[10] P. W. Shor, “Algorithms for quantum computation: Discrete logarithms and factoring,” in Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on. IEEE, 1994, pp. 124-134.

[11] L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing. ACM, 1996, pp. 212-219. [OpenAIRE]

[12] A. J. da Silva, T. B. Ludermir, and W. R. de Oliveira, “Quantum perceptron over a field and neural network architecture selection in a quantum computer,” Neural Networks, vol. 76, pp. 55 - 64, 2016.

[13] R. Zhou, H. Wang, Q. Wu, and Y. Shi, “Quantum associative neural network with nonlinear search algorithm,” International Journal of Theoretical Physics, vol. 51, no. 3, pp. 705-723, 2012.

[14] S. Gupta and R. Zia, “Quantum neural networks,” Journal of Computer and System Sciences, vol. 63, no. 3, pp. 355 - 383, 2001.

[15] M. Andrecut and M. Ali, “A quantum neural network model,” International Journal of Modern Physics C, vol. 13, no. 01, pp. 75-88, 2002.

36 references, page 1 of 3
Abstract
<jats:p>The learning process for multilayered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow–Hoff formula, do not change the eigenvectors of the weight matrix while flatting the eigenvalues. In infinity, these iterative formulas result in terms formed by the principal components of the weight matrix, namely, the eigenvectors corresponding to the non-zero eigenvalues. In quantum computing, the phase estimation algorithm is known to provide speedups over the conventional algorithms for the eigenvalue-related problems. Combining the quantum amplitude amplificat...
Subjects
ACM Computing Classification System: MathematicsofComputing_NUMERICALANALYSIS
free text keywords: Quantum Physics, Computer Science - Learning, Computer Science - Neural and Evolutionary Computing, Science, Q
36 references, page 1 of 3

[1] S. S. Haykin, Neural networks and learning machines. Pearson Upper Saddle River, NJ, USA:, 2009, vol. 3.

[2] H. Abdi, “Linear algebra for neural networks,” International encyclopedia of the social and behavioral sciences. Elsevier, Oxford UK, 2001.

[3] H. Abdi, D. Valentin, B. Edelman, and A. J. O'Toole, “More about the difference between men and women: evidence from linear neural networks and the principal-component approach,” Perception, vol. 24, no. 5, pp. 539-562, 1995.

[4] B. Widrow, M. E. Hoff et al., “Adaptive switching circuits,” in IRE WESCON convention record, vol. 4, no. 1. New York, 1960, pp. 96- 104. [OpenAIRE]

[5] H. Abdi, D. Valentin, B. Edelman, and A. J. O'Toole, “A widrow-hoff learning rule for a generalization of the linear auto-associator,” Journal of Mathematical Psychology, vol. 40, no. 2, pp. 175-182, 1996.

[6] S. Lloyd, “Ultimate physical limits to computation,” Nature, vol. 406, no. 6799, pp. 1047-1054, 2000.

[7] R. Feynman, “Simulating physics with computers,” International Journal of Theoretical Physics, vol. 21, pp. 467-488, 1982, 10.1007/BF02650179.

[8] C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, “Strengths and weaknesses of quantum computing,” SIAM Journal on Compututing, vol. 26, no. 5, pp. 1510-1523, 1997.

[9] D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proceedings of the Royal Society of London A: Mathematical and Physical Sciences, vol. 400, no. 1818, pp. 97-117, 1985.

[10] P. W. Shor, “Algorithms for quantum computation: Discrete logarithms and factoring,” in Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on. IEEE, 1994, pp. 124-134.

[11] L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing. ACM, 1996, pp. 212-219. [OpenAIRE]

[12] A. J. da Silva, T. B. Ludermir, and W. R. de Oliveira, “Quantum perceptron over a field and neural network architecture selection in a quantum computer,” Neural Networks, vol. 76, pp. 55 - 64, 2016.

[13] R. Zhou, H. Wang, Q. Wu, and Y. Shi, “Quantum associative neural network with nonlinear search algorithm,” International Journal of Theoretical Physics, vol. 51, no. 3, pp. 705-723, 2012.

[14] S. Gupta and R. Zia, “Quantum neural networks,” Journal of Computer and System Sciences, vol. 63, no. 3, pp. 355 - 383, 2001.

[15] M. Andrecut and M. Ali, “A quantum neural network model,” International Journal of Modern Physics C, vol. 13, no. 01, pp. 75-88, 2002.

36 references, page 1 of 3
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