  A cluster update (the ``operator-loop'') is developed within the framework of
a numerically exact quantum Monte Carlo method based on the power series
expansion of exp(-BH) (stochastic series expansion). The method is generally
applicable to a wide class of lattice Hamiltonians for which the expansion is
positive definite. For some important models the operator-loop algorithm is
more efficient than loop updates previously developed for ``worldline''
simulations. The method is here tested on a two-dimensional anisotropic
Heisenberg antiferromagnet in a magnetic field.
