A fundamental problem in quantum many-body physics is that of finding ground states of localHamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithmsfor learning ground states.

A fundamental problem in quantum many-body physics is that of finding ground states of localHamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithmsfor learning ground states. Science 2022], introduced an approach for learningproperties of the ground state of an n -qubit gapped local Hamiltonian H from only n {\mathcal{O}(1)} datapoints sampled from Hamiltonians in the same phase of matter. Nature Communications 2024], to \mathcal{O}(\log) samples when the geometry of the n -qubit system is known.In this work, we introduce two approaches that achieve a constant sample complexity, independentof system size n, for learning ground state properties. Our first algorithm consists of a simplemodification of the ML model used by Lewis et al. and applies to a property of interest known beforehand.