Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers

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 compressed many-body Hamiltonians that maintain the essential physics of strongly-correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here we demonstrate that utilizing quantum algorithms for obtaining the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate $\text{Ca}_2\text{CuO}_3$, the excitonic ground state of monolayer $\text{WTe}_2$, and the charge-ordered state of correlated metal $\text{SrVO}_3$. Numerical simulations utilizing a classical tensor network implementation of variational quantum eigensolvers allow us 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 these methods we demonstrate the potential of classical pre-optimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.