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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 (− β H)(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.