Most artificial neural networks are simulations, running on algorithmic computers. With this setup some of the inherent advantage of a neural network is lost; namely, the speed due to distributed computing. Clearly it would be better to utilize the intrinsic physics of a physical system to perform the computation. Many efforts have been expended in this direction, using systems ranging from nonlinear optical materials to proteins to DNA. At the same time, many other researchers have been exploring the possibility of building quantum computers. In previous work, using the real time evolution of quantum dot molecules, the investigators have shown by simulation that such an architecture could act as a recurrent temporal quantum neural network. Inputs were prepared by fixing the initial states of two such quantum dot molecules, and outputs determined by reading their values at a given time T later. The dot molecules were assumed to interact with the substrate phonons and with an externally applied time dependent electric field. Trainable parameters were the numbers of phonons, optically excited, their frequencies, and the value of the electric field as a function of time. This network could perform any classical logic gate, and, in addition, could calculate a purely quantum gate, for which there is no classical equivalent. Unfortunately the physical problems to be surmounted in actual construction of this device seemed beyond present technology. For example, the reading and writing of the final and initial states at sufficiently precise times, on this scale, might be very difficult.
This new project will explore by simulation the possibility of a spatial, rather than temporal, design. The new network will consist of a regular array of quantum dot molecules on a suitable substrate. The molecules interact with each other directly through Coulombic interactions and indirectly through their mutual interaction with local and phononic modes of the substrate. These modes can be preferentially excited by optical excitation, and, therefore, controlled externally. The number of excitations can thus be used as trainable "weight" parameters for a neural network. As with the temporal net, the spatial net has none of the "wiring problems" of traditional neural nets: the necessary connections are supplied by the physical system itself. The long range character of the phononic interactions takes the net beyond traditional connectionist structures.
This work will involve three successive phases. The first phase will be a complete rederivation of the neural net setup to the spatial case, in one and two dimensions, and an extension of the training algorithm from the temporal to the equilibrium state. The second will be the simulation of large networks of neurons, in one and two dimensions, to perform benchmark neural network tasks. The physical system will be progressively more accurately modeled, to include the effects of noise, defects, and finite temperature. The third will develop a backpropagation training scheme to enable the network to train itself and to develop a hardware implementation at the end of the project. A working quantum neural computer is expected to have wide application and interest. ***
