A quantum neural net: with applications to materials science

A 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 cross-product terms in internal representation of its basis functions introduced parsimoniously. These cross-products 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.