Quantum-mechanical tunneling in associative neural networks

We investigate the quantum-mechanical tunneling between the "patterns" of t he, so-called, associative neural networks. Being the relatively stable min ima of the "configuration-energy" space of the networks, the "patterns" rep resent the macroscopically distinguishable states of the neural nets. There fore, the tunneling represents a macroscopic quantum effect, but with some special characteristics. Particularly, we investigate the tunneling between the minima of approximately equal depth, thus requiring no energy exchange . If there are at least a few such minima: the tunneling represents a sort of the "random walk" process, which implies the quantum fluctuations in the system, and therefore "malfunctioning" in the information processing of th e nets. Due to the finite number of the minima, the "random walk" reduces t o a dynamics modeled by the, so-called, Pauli master equation. With some pl ausible assumptions, the set(s) of the Pauli master equations can be analyt ically solved. This way comes the main result of this paper: the quantum fl uctuations due to the quantum-mechanical tunneling can be "minimized" if th e "pattern"-formation is such that there are mutually "distant" groups of t he "patterns", thus providing the "zone" structure of the "pattern" formati on. This qualitative result can be considered as a basis of the efficient d eterministic functioning of the associative neural nets.