  An efficient Quantum Monte Carlo algorithm for the simulation of bosonic
systems on a lattice in a grand canonical ensemble is proposed. It is based on
the mapping of bosonic models to the spin models in the limit of the infinite
total spin quantum number. It is demonstrated, how this limit may be taken
explicitly in the algorithm, eliminating the systematic errors. The efficiency
of the algorithm is examined for the non-interacting lattice boson model and
compared with the stochastic series expansion method with the heat-bath type
scattering probability of the random walker.
