Dynamical Mean-Field Theory for Real Materials using Variational Quantum Compressed Time Evolution on a Quantum Computer

We design a hybrid quantum-classical computational workflow, combining density functional theory and dynamical mean-field theory, to investigate the electronic properties of CaCuO2, a parent structure of high-temperature cuprate superconductors. Our approach uses a quantum algorithm as an impurity solver that is based on variational quantum compressed time evolution to compute the time-dependent Greens function on an IBM Heron quantum device. Utilizing error mitigation techniques and a Lehmann representation fitting procedure, we extract the density of states from the signal in the accessible time regime. Despite the significant challenges rooted in the residual imprecision of currently accessible NISQ devices, we successfully resolve the characteristic features of the spectral function. However, we find that the required numerical accuracy for full DMFT self-consistency exceeds current hardware capabilities, indicating that practical real-material DMFT applications will necessitate post-NISQ hardware developments.