Designing ground states of Hopfield networks for quantum state preparation

Abstract: We present a protocol to store a polynomial number of arbitrary bit strings, encoded as spin configurations, in the approximately degenerate low-energy manifold of an all-to-all connected Ising spin glass. The iterative protocol is inspired by machine learning techniques utilizing $k$-local Hopfield networks trained with $k$-local Hebbian learning and unlearning. The trained Hamiltonian is the basis of a quantum state-preparation scheme to create quantum many-body superpositions with tunable squared amplitudes using resources available in near term experiments. We find that the number of configurations that can be stored in the ground states and thus turned into superposition scales with the $k$-locality of the Ising interaction.