Summary
We explore a model for a quantum Hopfield artificial neural network, in which qubits are prepared in an initial state and allowed to evolve to steady state. We derive the equations for finding their stable states, by minimizing the Lyapunov energy. We apply the equations first to the cytoskeleton of a biological neuron, where the qubits are microtubulins in a microtubule. Our method can reproduce classical calculations made earlier by Tuszynski et al., but because it is a fully quantum method can also explore the possibility that an artificial computing structure based on an array of tubulins can act as a quantum computer. We then derive a method for training the quantum network to converge to a stable target pattern, given an input pattern, and show that a spatial array of qubits can be trained to perform the CNOT, which with a rotation is a universal quantum gate. This means that a large enough array can in principle be trained to do any calculation.
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References
Behrman E C, Nash L R, Steck J E, Chandrashekar V G, Skinner S R (2000) Information Sciences 128:257-269
DeGaris H, Sriram R, Zhang Z (2003) Proceedings of the International Joint Conference on Neural Networks 4:2589-2593
Bandyopadhyay S, Menon L, Kouklin N, Williams P F, Ianno N J (2002) Smart Mater. Struc. 11:761-766
Ezhov A (2003) Proceedings of SPIE 5128:107-119
Resconi G, van del Wal A J (2002)Information Sciences 142:249-273
Allauddin R, Gaddam K, Behrman E C, Steck J E, Skinner S R (2002) Proceedings of the International Joint Conference on Neural Networks 3:2732-2737
Hopfield J J (1982) Proceedings of the National Academy of Sciences USA 79: 2554-2558
Haykin S (1999) Neural Networks: a Comprehensive Foundation. Prentice Hall, New York
Abu-Mostafa Y S, St. Jacques J-M (1985) IEEE Trans. Information Theory IT31:461-464
Tuszynski J A, Hameroff S, Hurylak P (1998) Phil Trans R. Soc. Lond. A 356:1897-1926
Hagan S, Hameroff S R, Tuszynski J A (2002) Phys. Rev. E 65:061901-11
Werbos P (1997) Handbook of Neural Computation, release 97/1, A2.3:2
Behrman E C, Jongeward G A, Wolynes P G (1983) J. Chem. Phys. 79:6277-6281
Behrman E C, Gaddam K, Steck J E, Skinner S R Microtubulins as a quantum Hopfield network. In Tuszynski JA (ed.) The Emerging Physics of Consciousness. Springer Verlag, 2006. This paper was written after, but published before, the present article, and contains an expanded and extended version of the method and results in section ??. Though published subsequently, we consider the present work to be the foundational paper.
Kac M (1968) Mathematical mechanisms of phase transitions. In Chretien M, Gross E, Deser S (eds.) Statistical Physics: Phase transitions and superfluidity. 1:241-305
Feynman R P, Hibbs A R (1965) Quantum Mechanics and Path Integrals. McGraw-Hill, New York
Polyak M (2004) arXiv: math.GT/0406251
Luenberger D G (1984) Linear and Nonlinear Programming. Addison-Wesley, Reading, MA
Zanardi P, Rasetti M (1997) arXiv: quant-ph/9705044
Nielsen M A, Chuang I L (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge, UK
Grover L K (1996) Proceedings of the 28th Annual ACM Symposium on Theory of Computing. ACM, New York, pp.212-9.
Shor P W (1997) SIAM J. Computing 26: 1484
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Allauddin, R., Boehmer, S., Behrman, E.C., Gaddam, K., Steck, J.E. (2008). Quantum Simulataneous Recurrent Networks for Content Addressable Memory. In: Nedjah, N., Coelho, L.d.S., Mourelle, L.d.M. (eds) Quantum Inspired Intelligent Systems. Studies in Computational Intelligence, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78532-3_3
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