A Quantum Neural Net : with Applications to Materials Science

In this article a new neural network architecture suitable for learning and generalization is discussed and developed. The architecture is inspired and modeled after quantum electronic devices and circuits where coherent electronic wavefunctions traveling through different parts of the circuit are combined together and result in interferences at detection nodes. These wavefunctions, represented by complex numbers, are implemented as complex weights in our neural net architecture to efficiently and accurately facilitate certain computations. Although similar to the radial basis function (RBF) net, our computational model called quantum net (QN) has demonstrated a considerable gain in performance and efficiency in number of applications compared to RBF net. Its better performance in classification tasks is explained by the crossproduct terms in internal representation of its basis functions introduced parsimoniously. These crossproducts are the results of interferences naturally occurring in coherent electronic systems. Although we primarily discuss the software implementation of QN on Von Neuman computers, its hardware implementation is also briefly discussed. A number of examples, solved using QN and other networks, are used to illustrate the desirable characteristics of QN. INTRODUCTION We explore a new computation method that we call “quantum network” (QN) that uses complex weights in a neural network lattice and can be constructed using quantum wires, dots, and other quantum electronic components. Using coherent electrons or other quantum particles to perform calculations, QN takes advantage of “interferences” that take place between these particles traveling through different paths in the circuit. These interferences are very well known in quantum mechanics and are basis of many physical phenomena such as conductivity of solids, tunnelings in quantum layers, optical properties of clusters, etc. Our QN is the subset of a more general class of computational models and techniques called quantum computers and quantum computing that has received a renewed interest in recent years [I]-[SI. The mathematical model, considered here, is an expansion in basis functions, that is, it connects the multivariate system input x and output y (which without loss of generality can be assumed univariate) by the equation N Y = f i E T (4 = c angn (X> b, 1 Y ,=I where a,,& are adjustable real parameters, g , are called basis functions. The types and the number of basis functions determine the architecture of the model, its accuracy and efficiency. The basis functions usually have the same structure for any n =1, N and constitute a superposition of a simple multivariate function cp of x and b, (internal function) and a univariate function g (external function), as shown in the equation In neural networks and RBF networks the internal function cp is a linear sum of univariate functions 0-7803-5489-3/99/$10.00 01999 IEEE.