  Working within the stochastic series expansion framework, we introduce and
characterize a new quantum cluster algorithm for quantum Monte Carlo
simulations of transverse field Ising models with frustrated Ising exchange
interactions. As a demonstration of the capabilities of this new algorithm, we
show that a relatively small, ferromagnetic next-nearest neighbour coupling
drives the transverse field Ising antiferromagnet on the triangular lattice
from an antiferromagnetic three-sublattice ordered state at low temperature to
a ferrimagnetic three-sublattice ordered state.
