  Tensor networks have recently found applications in machine learning for both
supervised learning and unsupervised learning. The most common approaches for
training these models are gradient descent methods. In this work, we consider
an alternative training scheme utilizing basic tensor network operations, e.g.,
summation and compression. The training algorithm is based on compressing the
superposition state constructed from all the training data in product state
representation. The algorithm could be parallelized easily and only iterates
through the dataset once. Hence, it serves as a pre-training algorithm. We
benchmark the algorithm on the MNIST dataset and show reasonable results for
generating new images and classification tasks. Furthermore, we provide an
interpretation of the algorithm as a compressed quantum kernel density
estimation for the probability amplitude of input data.
