I had been vaguely aware that there was an important connection between tensor network representations of quantum many-body states (e.g., matrix product states) and artificial neural nets, but it didn’t really click together until I saw Roger Melko’s nice talk on Friday about his recent paper with Torlai et al.:a
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In particular, he sketched the essential equivalence between matrix product states (MPS) and restricted Boltzmann machinesb (RBM) before showing how he and collaborators could train an efficient RBM representations of the states of the transverse-field Ising and XXZ models with a small number of local measurements from the true state.
As you’ve heard me belabor ad nauseum, I think identifying and defining branches is the key outstanding task inhibiting progress in resolving the measurement problem. I had already been thinking of branches as a sort of “global” tensor in an MPS, i.e., there would be a single index (bond) that would label the branches and serve to efficiently encode a pure state with long-range entanglement due to the amplification that defines a physical measurement process. (More generally, you can imagine branching events with effects that haven’t propagated outside of some region, such as the light-cone or Lieb-Robinson bound, and you might even make a hand-wavy connection to entanglement renormalization.)… [continue reading]