We perform a systematic study of preparing ground states of correlated
multi-orbital impurity models using variational quantum eigensolvers (VQEs). We
consider both fixed and adaptive wavefunction ans\"atze and analyze the
resulting gate depths and the performance with and without noise. For the
adaptive procedure, we develop an operator pool consisting of pairwise
commutators of Hamiltonian terms that allows for a fair comparison between the
adaptive and fixed Hamiltonian variational ansatz. Using noiseless statevector
simulations, we find that the most compact ans\"atze are obtained in an atomic
orbital representation and using parity encoding. Focusing on the adaptive
algorithms, which yield the circuits with the least number of CNOTs, we then
show that in the presence of sampling noise, high-fidelity state preparation
can still be achieved with the Hamiltonian commutator pool. By utilizing
Hamiltonian integral factorization and a noise resilient optimizer, we show
that this approach requires only a modest number of about 212 shots per
measurement circuit. We discover a dichotomy of the operator pool complexity in
the presence of sampling noise, where a small pool size reduces the adaptive
overhead but a larger pool size accelerates convergence to the ground state.
When considering realistic gate noise in addition, we observe that the variable
optimization can still be performed as long as the two-qubit gate error lies
below 10−3, which is close but below current hardware levels. Finally, we
measure the ground state energy of the eg model on IBM and Quantinuum
quantum hardware using the converged adaptive ansatz. We perform a systematic
error mitigation analysis on the IBM results and obtain a relative error of
0.7\% using symmetry-based postselection and zero-noise extrapolation (ZNE).Comment: 19 pages, 9 figure