Adiabatic quantum algorithm for the Bose-Hubbard model

Abstract

In recent years research has been carried out on algorithms to simulate quantum many body systems in current NISQ devices. In particular, for the ground state finding problem, known to be QMA-complete, a quantum adiabatic algorithm can be used. On the other hand, the Bose-Hubbard model has gained impact lately because of the prediction of exotic phases of matter and because its experimental realisation in a set up with cold atoms in optical lattices. In this work, an adiabatic quantum algorithm is designed to obtain the ground state of a one-dimensional Bose-Hubbard model. The three parts of the algorithm are presented: initial state preparation, adiabatic evolution and measurement. The results presented correspond to a system of 2 sites and NP particles, although the algorithm has been tested for systems with more sites. The algorithm has been tested by performing simulations