Number-state preserving tensor networks as classifiers for supervised learning

We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This is argued to be natural choice classifiers as 1) they map classical data data, and thus preserve the interpretability under transformations, 2) can efficiently trained maximize their scalar product against sets, 3) seem powerful generic (unrestricted) networks in this task. Our proposal demonstrated using variety benchmark classification problems, where versions commonly used (including MPS, TTN MERA) are effective classifiers. work opens path methods such MERA, which were previously computationally intractable classifiers, employed difficult tasks image recognition.