  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 $0.7\%$.
