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

Abstract

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

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• A framework for efficient ab initio electronic structure with Gaussian Process States
• Learning ground states of gapped quantum Hamiltonians with Kernel Methods
• Impact of conditional modelling for a universal autoregressive quantum state
• Boltzmann machines and quantum many-body problems
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Gaussian Processes for Finite Size Extrapolation of Many-Body Simulations