Compact quantum circuits of variational quantum eigensolver for quantum impurity models

The dynamical mean-field theory (DMFT) is a local approximation theory where the entire system is divided into correlated atoms and an environment representing the rest of the system. The biggest bottleneck of DMFT calculations is solving a quantum impurity model consisting of correlated sites (orbitals) and non-interacting bath sites representing the environment. The impurity models typically include bath sites more than correlated orbitals by one order of magnitude. Solving this model takes exponential computational costs for classical computers.

Variational quantum algorithms combining quantum and classical computers have been proposed to solve the above models in polynomial time. However, solving realistic models with multiple correlated sites is still too expensive with a near-term quantum device due to many variational parameters, especially for the bath sites.

We propose compact, physically motivated ansatzes by taking advantage of the fact that there are no direct interactions/hopping between their bath sites. The proposed ansatzes can reduce variational parameters for the bath sites. Using a quantum circuit simulator, we benchmark the proposed ansatzes against conventional ones, such as the unitary coupled-cluster ansatzes and the hardware-friendly ansatzes. We will show that the proposed ansatzes can accurately describe the ground states of impurity models with one correlated site. If time is allowed, we will show the results of impurity models with two correlated impurity sites.