A recurrent quantum neural network model to describe eye tracking of moving targets (2005)
Author: L. Behera, I. Kar, A.C. Elitzur

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A theoretical quantum neural network model is proposed using a
nonlinear Schrodinger wave equation. The model proposes that there
exists a nonlinear Schrodinger wave equation that mediates the col-
lective response of a neural lattice. The model is used to explain eye
movements when tracking moving targets. Using a Recurrent Quantum
Neural Network(RQNN) while simulating the eye tracking model, two
very interesting phenomena are observed. First, as eye sensor data is
processed in a classical neural network, a wave packet is triggered in
the quantum neural network. This wave packet moves like a particle.
Second, when the eye tracks a fixed target, this wave packet moves
not in a continuous but rather in a discrete mode. This result reminds
one of the saccadic movements of the eye consisting of ’jumps’ and
’rests’. However, such a saccadic movement is intertwined with smooth
pursuit movements when the eye has to track a dynamic trajectory. In
a sense, this is the first theoretical model explaining the experimental
observation reported concerning eye movements in a static scene situa-
tion. The resulting prediction is foundto bevery precise and efficient in
comparison to classical objective modeling schemes such as the Kalmanlter.

Key words: nonlinear Schr odinger wave equation, quantum dynamics,
saccadic eye movements, neural network, quantum computation