Semiclassical Neural Network

The classical integrate-and-fire neural network has been studied both in the simpler zero-width [1] action potential and the more involved finite-width [2]cases. In these works every neuron integrates the current coming from neighboring neurons and when the threshold for firing is exceeded, it too sends off an action potential to its neighbors. Hopfield and Herz had found that there is a simple relation between the contributions A from the neighbors and an external current I, with the time period of the firing of the network when phase-lock is established: τ (1 A)/I (1) It has been shown [2] that there is some modification of this formula when the action potential is not exactly a delta function but is spread over time, which is, of course, a more realistic assumption, in biological as well as physical contexts. In view of the recent great interest in quantum computing we think it is worthwhile to investigate the changes if any that would result from converting such networks to a quantum model. As a first step, we have here tried to see the changes when the action potential acts like a quantum radiation to the neighbors, instead of a current, and the firing of the neuron is replaced by induced radiation from it to the neighbors.