Evaluating a quantum Impurity solver for the single-impurity Anderson model with particle-hole symmetry

We investigate the performance of a quantum impurity solver applied to single-impurity Anderson models (SIAMs) with particle–hole symmetry. The solver's workflow begins with the use of the variational quantum Eigensolver to determine the model's ground state by optimizing a symmetry-preserving ansatz preparing half-filled state with zero spin projection. The same set of optimized parameters is then employed to prepare the particle and hole excitations required for the computation of the impurity Green's function. By avoiding additional optimization steps for these excited states, the method significantly reduces the computational overhead. Subsequently, the Lanczos coefficients defining the continued-fraction representation of the Green's function are approximated truncating their cumulant expansions, computed from expectation values of powers of the Hamiltonian on the excited states. We perform simulations for SIAMs with one, three, and five bath sites to explore how the accuracy and resource requirements of the solver evolve with system size. The results provide insight into the trade-offs between fidelity and computational cost, offering a first assessment of the scalability of hybrid quantum–classical approaches for solving impurity problems in strongly correlated electron systems.