Fig. 1: Model Hamiltonian approach to quantum simulation of strongly correlated matter.

a, The procedure starts with a description of the target molecule or material structure, whose electronic structure problem is reduced using classical computational chemistry techniques to a simpler effective Hamiltonian that captures the relevant low-energy behaviours. b, Here, we study problems that are modelled by spin Hamiltonians with potentially non-local connectivity and generic on-site spin S ≥ 1/2, where each spin is composed of localized, unpaired electrons in the original molecule. The key simplification comes from capturing charge fluctuations perturbatively, which is a good approximation in certain contexts. c, Programmable quantum simulation is then used to calculate properties of the model Hamiltonian. We develop a simulation framework, based on encoding spins into clusters of qubits, that can be readily implemented on existing hardware. The toolbox enables efficient generation of complex spin interactions by leveraging dynamical reconfigurability and hardware-optimized multi-qubit gates (Figs. 2 and 3). The quantum simulator performs time evolution under the spin Hamiltonian for various simulation times t, and each qubit is projectively measured to produce an set of snapshots. Subsequent classical processing extracts properties such as the low-lying excitation spectrum and magnetic susceptibilities, all from the same dataset (Figs. 4–6).