Several classical techniques have evolved over the years for the purpose of denoising binary images.But the main disadvantages of these classical techniques lie in that an a priori information regarding the noise characteristics is required during the extraction process. Among the intelligent techniques in vogue, the multilayer self organizing neural network (MLSONN) architecture is suitable for binary image preprocessing tasks.In this article, we propose a quantum version of the MLSONN architecture. Similar to the MLSONN architecture, the proposed quantum multilayer self organizing neural network (QMLSONN) architecture comprises three processing layers viz., input, hidden and output layers. The different layers contains qubit based neurons. Single qubit rotation gates are designated as the network layer interconnection weights.A quantum measurement at the output layer destroys the quantum states of the processed information thereby inducing incorporation of linear indices of fuzziness as the network system errors used to adjust network interconnection weights through a quantum backpropagation algorithm. Results of application of the proposed QMLSONN are demonstrated on a synthetic and a real life binary image with varying degrees of Gaussian and uniform noise. A comparative study with the results obtained with the MLSONN architecture and the supervised Hopfield network reveals that the QMLSONN outperforms the MLSONN and the Hopfield network in terms of the computation time.