QUANTUM ALGORITHMS WITH CONTROLLED HODGKIN-HUXLEY NEURONS

Abstract

The dynamical system corresponding to the Hodgkin-Huxley (HH) neuron contains the control parameter, for instance, the electrical current or another external signal, stimulating the action potential (outcome) in the axon. Choosing the appropriate shape of the control via speed gradient or alternative algorithms one can keep the system imitating a quantum behaviour. The controlled four-dimensional HH system, in this case, involves effects similar to the quantum phase contributions to the computational process. We provide a simple example of the HH-based computational algorithm following the quantum paradigm. The linear chain of two HH neurons emulates the results of the Deutsch – Jozsa algorithm for the searching problem. To reproduce the output effect similar to the contribution of quantum phases the neurons are controlled by one of two alternative feedback versions: target attractor or speed gradient. We invent the successful classical emulation of the Deutch-type quantum algorithm and discuss the pros and cons of both alternative feedback methods. Our approach can open a novel method for the practical realization of quantum algorithms and develop new perspectives for the computational properties of artificial neural networks (ANNs). The possible applications of the proposed algorithms are the modelling of epilepsy in the ANNs and the big data analysis.