Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models

Abstract

Hybrid quantum-classical embedding methods for correlated materials simulations provide a path towards potential quantum advantage. However, the required quantum resources arising from the multi-band nature of d and f electron materials remain largely unexplored. Here we compare the performance of different variational quantum eigensolvers in ground state preparation for interacting multi-orbital embedding impurity models, which is the computationally most demanding step in quantum embedding theories. Focusing on adaptive algorithms and models with 8 spin-orbitals, we show that state preparation with fidelities better than 99.9% can be achieved using about 2 14 shots per measurement circuit. When including gate noise, we observe that parameter optimizations can still be performed if the two-qubit gate error lies below 10 −3 , which is slightly smaller than current hardware levels. Finally, we measure the ground state energy on IBM and Quantinuum hardware using a converged adaptive ansatz and obtain a relative error of 0.7%. Quantum embedding approaches to simulate condensed matter on quantum computers have been proposed, yet applications are limited to simplest models. The authors perform a systematic study of ground state preparation with variational quantum algorithms for correlated multi-orbital impurity models, addressing key issues toward real materials simulations.