  A Monte Carlo method for quantum spin systems is formulated in the basis of
valence bond (singlet pair) states. The non-orthogonality of this basis allows
for an efficient importance-sampled projection of the ground state out of an
arbitrary state. The method provides access to resonating valence-bond physics,
enables a direct improved estimator for the singlet-triplet gap, and extends
the class of models that can be studied without negative-sign problems. As a
demonstration, the valence bond distribution in the ground state of the 2D
Heisenberg antiferromagnet is calculated. Generalizations of the method to
fermion systems are also discussed.
