Quantum Ans#X00e4;Tze for Green's Functions of Single-Impurity Anderson Models at Half-Filling

We introduce a set of quantum ansätze tailored for computing Green's functions of single-impurity models using the variational quantum eigensolver. These ansätze conserve particle number and spin, allowing for the efficient preparation of the impurity model's ground state and the Krylov bases required to express the Green's function as a continued fraction. Notably, the parameters preparing the particle and hole excitations used as initial Krylov vectors are fully determined by those optimized for the ground state, eliminating the need for secondary optimizations or alternative excitation preparation methods. We demonstrate the utility of these ansätze by computing Green's functions for single-impurity Anderson models with one bath site within a dynamical mean-field theory loop, where the impuritybath hybridization is updated self-consistently. The parameters defining the states in the Krylov bases are straightforwardly determined by orthonormality in the single-bath case, allowing for the direct computation of the relevant Hamiltonian matrix elements from these states. Future work will explore the robustness, scalability, and practical integration of these ansätze into hybrid quantum-classical simulations of strongly correlated materials.