  We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models.
In the special case of $S=1/2$, the new algorithm can be viewed as a cluster
algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$
model in two dimensions with a representation in which the quantization axis
lies in the easy plane. We find that the numerical autocorrelation time for the
cluster algorithm remains of the order of unity and does not show any
significant dependence on the temperature, the system size, or the Trotter
number. On the other hand, the autocorrelation time for the conventional
algorithm strongly depends on these parameters and can be very large. The use
of improved estimators for thermodynamic averages further enhances the
efficiency of the new algorithms.
