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Brain-computer interface (BCI) technology is a means of communication that allows individuals with severe movement disability to communicate with external assistive devices using the electroencephalogram (EEG) or other brain signals. This paper presents an alternative neural information processing architecture using the Schrödinger wave equation (SWE) for enhancement of the raw EEG signal. The raw EEG signal obtained during the motor imagery (MI) of a BCI user is intrinsically embedded with non-Gaussian noise while the actual signal is still a mystery. The proposed work in the field of recurrent quantum neural network (RQNN) is designed to filter such non-Gaussian noise using an unsupervised learning scheme without making any assumption about the signal type. The proposed learning architecture has been modified to do away with the Hebbian learning associated with the existing RQNN architecture as this learning scheme was found to be unstable for complex signals such as EEG. Besides, this the soliton behaviour of the non-linear SWE was not properly preserved in the existing scheme. The unsupervised learning algorithm proposed in this paper is able to efficiently capture the statistical behaviour of the input signal while making the algorithm robust to parametric sensitivity. This denoised EEG signal is then fed as an input to the feature extractor to obtain the Hjorth features. These features are then used to train a Linear Discriminant Analysis (LDA) classifier. It is shown that the accuracy of the classifier output over the training and the evaluation datasets using the filtered EEG is much higher compared to that using the raw EEG signal. The improvement in classification accuracy computed over nine subjects is found to be statistically significant.