We are witnessing an exciting interplay between physics, computation and neurobiology that spans in multiple directions. In one direction we can use the power of complex systems analysis, developed in theoretical physics and applied mathematics, to elucidate design principles governing how neural networks, both biological and artificial, can learn and function. In another direction, we can exploit novel physics to instantiate and analyze new kinds of quantum neuromorphic computers built using atomic spins and photons. We will give several vignettes in both directions, including: (1) deriving the detailed structure of the primate retina from first principles by developing optimal neural networks for processing natural movies, (2) using dynamic mean field theory to understand and optimize the training of deep neural networks used in machine learning, (3) understanding the geometry and dynamics of high dimensional optimization in the classical limit of a dissipative many-body quantum optimizer comprised of interacting photons.

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