Inverse Design of Many-Body Hamiltonians on Programmable Quantum Devices

Recent advances in quantum learning theory have shown that local Hamiltonians can be efficiently recovered from a single eigenstate, with significant implications for verifying programmable quantum devices and analyzing correlated phases of matter. In this work, we integrate Hamiltonian learning techniques with variational state preparation to design many-body Hamiltonians that yield equilibrium states with tailored target properties. Our approach involves first optimizing specific order parameters over a family of variational states, followed by learning the Hamiltonian that includes the prepared states in its low-energy manifold. We validate this method numerically in the context of programmable fermionic quantum simulators, designing Hamiltonians that enhance superconducting pair correlations at finite temperatures. Additionally, we explore extensions to non-equilibrium properties in quantum chemistry, such as designing complex molecular interactions that optimize specific dynamic response functions.