量子联想网络.pdf

NEURAL NETWORKS AS A BASIS FOR QUANTUM ASSOCIATIVE NETWORKS MITJA PERUSˇ Institute BION, Stegne 21, SLO-1000 Ljubljana, Slovenia mitja.perus@uni-lj.si Published in: NEURAL NETWORK WORLD vol. 10 (2000) pp. 1001-1013. Abstract We have got a lot of experience with computer simulations of Hop?eld’s and holo- graphic neural net models. Starting with these models, an analogous quantum in- formation processing system, called quantum associative network, is presented in this article. It was obtained by translating an associative neural net model into the mathe- matical formalism of quantum theory in order to enable microphysical implementation of associative memory and pattern recognition. In a case of successful quantum im- plementation of the model, expected bene?ts would be signi?cant increase in speed, in miniaturization, in e?ciency of performance, and in memory capacity, mainly because of additionally exploiting quantum-phase encoding. Keywords: Hop?eld model, associative neural network, quantum associative network, holography, quantum computing 1 Introduction In previous articles [1, 2, 3] we have presented in detail how and where the mathematical formalism of associative neural network models by Hop?eld [4] and Haken [5] is analogous to the mathematical formalism of quantum theory (similar comparative studies can be found in [6, 7, 8]). In this article, an original and fundamental information processing system is pre- sented, and an example of a quantum neural-network-like information processing “algorithm” is described in a way understandable for computer scientists, physicists and neuroscientists. We have chosen this “algorithm”, simple but nevertheless e?ective, technically realizable, and roughly (on global scale) bio