# A Quantum Implementation Model for Artificial Neural Networks

- Published: 19 Sep 2016 Journal: Quanta, volume 7, page 7 (eissn: 1314-7374, Copyright policy)
- Publisher: Quanta

[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.

###### Related research

[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.