Occupation-number quantum-subspace-expansion approach to computing the single-particle Green function: An opportunity for noise filtering

We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy intermediate-scale quantum (NISQ) devices. The technique consists in the construction of a nonorthogonal excitation basis composed of a set of single-particle excitations generated by occupation-number operators. The excited sectors of the Hamiltonian in this basis can then be measured on the quantum device and a classical postprocessing procedure yields the Green function in the Lehmann representation. The technique allows for noise filtering, a useful feature for NISQ devices. To validate the approach, we carry out a set of proof-of-principle calculations on the single-band Hubbard model on IBM quantum hardware. For a two-site system we find good agreement between the results of quantum simulations and the exact result for the local spectral function. This proof of principle also shows that the noise filtering provides a reliable way to get rid of satellite peaks present in the spectral weight obtained from a NISQ device. A simulation of a four-site system carried out on classical hardware suggests that the approach can achieve similar accuracy for larger systems.