Variational quantum-algorithm based self-consistent calculations for the two-site DMFT model on noisy quantum computing hardware

Abstract: Dynamical Mean Field Theory (DMFT) is one of the powerful computational approaches to study electron correlation effects in solid-state materials and molecules. Its practical applicability is, however, limited by the quantity of numerical resources required for the solution of the underlying auxiliary Anderson impurity model. Here, the one-to-one mapping between electronic orbitals and the state of a qubit register suggests a significant computational advantage for the use of a Quantum Computer (QC) for solving this task. In this work we present a QC approach to solve a two-site DMFT model based on the Variational Quantum Eigensolver (VQE) algorithm. We analyse the propagation of stachastic and device errors through the algorithm and their effects on the calculated self-energy. Therefore, we systematically compare results obtained on simulators with calculations on the IBMQ Ehningen QC hardware. We suggest a means to overcome unphysical features in the self-energy which already result from purely stochastic noise. Based heron, we demonstrate the feasibility to obtain self-consistent results of the two-site DMFT model based on VQE simulations with a finite number of shots.