In search for a possible connection between quantum computing and neural computation

This  topic arises from the recent interest in quantum computing. The main features of this new way of computation are reversible computing and the superposition principle valid for quantum states. The ensuing quantum parallelism engenders new classes of algorithms for the solution of NP-hard problems.

The practical realization of real quantum computers seems still far away mainly because of the extreme instability of coherent quantum states. On the other hand, Gershenfeld recently has given a practical approach to quantum computing in liquids at normal temperatures. In my opinion these recent developments challenge the investigation of algorithms based on reversible computing principles while exploiting the superposition of states (quantum algorithms). I therefore investigate quantum algorithms for the control of robots (artificial ant with a ``quantum brain'' consisting of a few spins) and for simple logic inference procedures.

On a more speculative level one may pursue the question whether the superposition principle might be of relevance also for brain states. Viewing as I  do the brain as a classical system this idea makes sense only if one can establish a quantum level of description in a classical system. Of course the former can live only as an approximation since true nonlocality can not exist in a classical system. However, "normal" quantum effects should be not too strange for a classical system of sufficient complexity. In fact, many years ago, David Bohm has tried to obtain quantum theory as an emergent property in a self-similar hierarchical system of classical oscillators. This has long been ignored but his approach sees a renaissance very recently which underlines the relevance of this model.

Bohm's hypothetical system shares some similarities with certain microscopic models of brain dynamics based on modeling the neuron as a relaxation oscillator (integrate-and-fire models in the simplest case). In view of the similarity between the two models one may speculate that at a certain mesoscopic or macroscopic level of description brain states are represented best as vectors in Hilbert space. This introduces superposition of states and a kind of quantum parallelism as an option for brain dynamics. Although this idea is highly speculative it seems worthwhile pursuing it since it opens a completely new way to understand information processing in the brain.


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