  We study a soliton in an optical lattice holding bosonic atoms quantum
mechanically using both an exact numerical solution and quantum Monte Carlo
simulations. The computation of the state is combined with an explicit account
of the measurements of the numbers of the atoms at the lattice sites. In
particular, importance sampling in the quantum Monte Carlo method arguably
produces faithful simulations of individual experiments. Even though the
quantum state is invariant under lattice translations, an experiment may show a
noisy version of the localized classical soliton.
