Variational Quantum Simulations of Multi-Orbital Impurity Models*

We perform a systematic study of preparing ground states of correlated multi-orbital impurity models using the variational quantum eigensolver (VQE). We consider both fixed and adaptive wavefunction ans\"atze and analyze the resulting gate depths and performance. We analyze the qubit-adaptive VQE algorithm in the Hartree-Fock orbital basis, as well as the Hamiltonian variational ansatz (HVA) and a variant of adaptive VQE in the atomic orbital basis. 

An operator pool composed of pairwise commutators of the Hamiltonian terms is developed to allow a fair comparison between the adaptive and the fixed HVA ansatz. Using state vector simulations, we show that the most compact ans\"atze is obtained in the atomic orbital representation with symmetry-based Pauli tapering within parity encoding. Finally, we perform adaptive VQE calculations including sampling noise and demonstrate that using a doubly decomposed form of the impurity Hamiltonian, symmetry-based qubit reduction, and stochastic optimizers dramatically reduces the number of shots required for the desired accuracy.