Effective calculation of the Green's function in the time domain on near-term quantum processors

Understand

We propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models.

• This novel protocol significantly reduces the number of controlled operations when compared to those previously suggested in literature.
• Such reduction is quite remarkable when considering the 2-site Hubbard model, for which we show that it is possible to obtain the exact time propagation of the $|N\pm 1\rangle$ states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.