Hybrid quantum-classical simulations of correlated materials within Gutzwiller variational approach

We develop a hybrid quantum-classical simulation framework that leverages existing noisy intermediate-scale quantum (NISQ) computing technology to study ground-state properties of correlated electron materials. It combines classical Gutzwiller variational embedding theory with state-of-the-art quantum computing algorithms to solve the effective multi-orbital embedding problem. The theory amounts to finding a self-consistent solution of coupled eigenvalue equations. The effective quasi-particle Hamiltonian is diagonalized efficiently using classical computers, while the ground state of the Gutzwiller embedding Hamiltonian is obtained using variational quantum eigensolvers implemented on quantum computing devices. This is feasible on NISQ devices and takes advantage of relatively shallow quantum circuits for error mitigation. The approach is applied to the periodic Anderson model and Hubbard models. Various variational ansatz and quantum noise forms will be compared on their numerical convergence and calculation accuracy.