  We report on results of Quantum Monte Carlo simulations for bosons in a two
dimensional quasi-periodic optical lattice. We study the ground state phase
diagram at unity filling and confirm the existence of three phases: superfluid,
Mott insulator, and Bose glass. At lower interaction strength, we find that
sizable disorder strength is needed in order to destroy superfluidity in favor
of the Bose glass. On the other hand, at large enough interaction superfluidity
is completely destroyed in favor of the Mott insulator (at lower disorder
strength) or the Bose glass (at larger disorder strength). At intermediate
interactions, the system undergoes an insulator to superfluid transition upon
increasing the disorder, while a further increase of disorder strength drives
the superfluid to Bose glass phase transition. While we are not able to discern
between the Mott insulator and the Bose glass at intermediate interactions, we
study the transition between these two phases at larger interaction strength
and, unlike what reported in arXiv:1110.3213v3 for random disorder, find no
evidence of a Mott-glass-like behavior.
