Ground States of Strongly-Correlated Materials on Quantum Computers Using Ab Initio Downfolding

The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving accurate many-body Hamiltonians including strong correlations, representing a subspace of interest of a material, using density functional theory calculations as a starting point. However, the solution of these material-specific models can scale exponentially on classical computers, constituting a challenge. Here we propose that utilizing quantum computers for obtaining the properties of downfolded Hamiltonians yields an accurate description of the ground state properties of strongly-correlated systems, while circumventing the exponential scaling problem. We demonstrate this for diverse strongly-correlated materials by combining ab initio downfolding and variational quantum eigensolvers, correctly predicting the antiferromagnetic state of one-dimensional cuprate Ca_2CuO_3, the excitonic ground state of monolayer WTe_2, and the charge-ordered state of correlated metal SrVO_3. By utilizing a classical tensor network implementation of variational quantum eigensolvers we are able to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address.