Multi-site gates for state preparation in quantum simulation of the Bose Hubbard Model

We construct a sequence of multi-site gates which transform an easily constructed product state into an approximation to the superfluid ground state of the Bose-Hubbard model. The mapping is exact in the one dimensional hard core limit, and for non-interacting particles in both one and two dimensions. The gate sequence has other applications, such as being used as part of a many-body interferometer which probes the existence of doublons.