Measurement based quantum algorithm for ground state preparation.

In this presentation we will present a quantum algorithm for state preparation that uses time evolution along with repeated measurement scheme to obtain the ground state of a Hamiltonian with known energies for the ground and first excited state. We show its implementation on current simulators for both the two-dimensional Heisenberg model and the phenomenological nuclear shell model and we compare its performance with other methods that make use of Linear Combination of Unitaries, previously developed in the literature.