Tensor Networks: Putting Quantum Wavefunctions into Machine Learning

If you follow machine learning, you have definitely heard of neural networks. If you are a physicist, you may have heard of tensor networks too. Both are schemes for assembling simple units (neurons or tensors) into complicated functions: decision functions in the case of machine learning or wavefunctions in the case of quantum mechanics. But tensor networks have only linear elements. Neural networks crucially require non-linear elements for their success (specifically, non-linear neuron activation functions).