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We introduce the quantum Gaussian process state, motivated via a statisticalinference for the wave function supported by a data set of unentangled productstates. We show that this condenses down to a compact and expressive parametricform, with a variational flexibility shown to be competitive or surpassingestablished alternatives. The connections of the state to its roots as aBayesian inference machine as well as matrix product states, also allow forefficient deterministic training of global states from small training data withenhanced generalization, including on application to frustrated spin physics.

The quantum Gaussian process state: A kernel-inspired state with quantum support data