  Simulations of frustrated quantum antiferromagnets suffer from a severe sign
problem. We solve the ergodicity problem of the loop-cluster algorithm in a
natural way and apply a powerful strategy to address the sign problem. For the
spin 1/2 Heisenberg antiferromagnet on a kagome and on a frustrated square
lattice, a nested cluster algorithm eliminates the sign problem for large
systems. The method is applicable to general lattice geometries but limited to
moderate temperatures.
