  A quantum world-line Monte Carlo method for high-symmetrical quantum models
is proposed. Firstly, based on a representation of a partition function using
the Matsubara formula, the principle of quantum world-line Monte Carlo methods
is briefly outlined and a new algorithm using non-binary loops is given for
quantum models with high symmetry as SU(N). The algorithm is called non-binary
loop algorithm because of non-binary loop updatings. Secondary, one example of
our numerical studies using the non-binary loop updating is shown. It is the
problem of the ground state of two-dimensional SU(N) anti-ferromagnets. Our
numerical study confirms that the ground state in the small N <= 4 case is a
magnetic ordered Neel state, but the one in the large N >= 5 case has no
magnetic order, and it becomes a dimer state.
