Quantum digital simulation of three toy models using IBM quantum hardware.

Using the phase estimation algorithm it is possible, in principle, to obtain the eigenstates of a large family of many-body Hamiltonians. In this talk we will present the results of our attempts to implement phase estimation algorithms to obtain the eigenvalues of 3 simple model Hamiltonians, using IBM quantum hardware. For that matter, we have considered a two level system, a two site Ising model with longitudinal magnetic field, and a two site Hubbar model at half filling. We have made use of both the phase estimationa and iterative phase estimation algorithms. We have explored to which point the unwanted hardware noise compromises the accuracy of the algorithm. In the case of the Hubbard model, for which a Troterization procedure is required, we study the optimal number of Trotter steps. Our results illustrate the limits of the phase estimation approach for quantum digital simulation in state of the art hardware.