Title: Towards Quantum Inspired Convolution Networks. Abstract: Deep Convolution Neural Networks (CNNs), rooted by the pioneer work of  \cite{Hinton1986,LeCun1985,Alex2012}, and summarized in \cite{LeCunBengioHinton2015},   have been shown to be very useful in a variety of fields.  The  state-of-the art CNN machines such as image rest net \cite{He_2016_CVPR} are described by real value inputs and kernel convolutions followed by the local and  non-linear rectified linear outputs.  Understanding the role of these layers, the accuracy and limitations of them,  as well as making them more efficient (fewer parameters)  are all ongoing research questions. 
 
 Inspired in quantum theory, we propose the use of complex value kernel functions, followed by the local non-linear  absolute (modulus) operator square. We argue that an advantage of quantum inspired complex kernels is robustness to realistic unpredictable scenarios (such as clutter noise,  data deformations). We study a concrete problem of shape detection and show that when multiple overlapping shapes are deformed and/or clutter noise is added, a convolution layer with quantum inspired complex kernels outperforms the statistical/classical kernel counterpart and a "Bayesian shape estimator" . The superior performance is due to the quantum phenomena of interference, not present in classical CNNs.  