  We present a new method to study the ground state of quantum spin systems
using the Monte Carlo techniques together with restructured intermediate states
which we proposed previously.
  Our basic idea is to obtain coefficients in the expansion of the ground state
from measurements of the normalized frequencies of each state on the boundary
in the Trotter direction. The restructuring method we have proposed makes it
possible to carry out simulations within available resources of computers.
  For a concrete example we study ladder spin systems with antiferromagnetic
intra-chain nearest neighbor interactions, whose ground states may be
equivalent to that of the spin 1 chain. For the ladder with ferromagnetic rungs
we successfully show how to determine the magnitudes and relative signs of the
coefficients in the expansion. When the ladder has antiferromagnetic rungs we
examine White's claim that the diagonally situated pair of spins are mostly
triplet states in the ground state. Our results strongly suggest that the
system has the hidden order which is constructed by the specially aligned
triplet states of diagonal pairs.
