Simulating complex materials science problems on quantum computers and finding best practices for optimization and ansatz selection

The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Various ab initio compression techniques have emerged as a way of deriving accurate many-body Hamiltonians including strong correlations, 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 compressed Hamiltonians can yield accurate descriptions of the ground state properties of strongly-correlated systems. We demonstrate how the variational quantum eigensolver can be used to correctly predict ground state properties of diverse strongly-correlated materials. 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. Through our studies we have developed various best practices for optimization and ansatz selection that we will discuss in this talk.