  We formulate a quantum Monte Carlo (QMC) method for calculating the ground
state of many-boson systems. The method is based on a field-theoretical
approach, and is closely related to existing fermion auxiliary-field QMC
methods which are applied in several fields of physics. The ground-state
projection is implemented as a branching random walk in the space of permanents
consisting of identical single-particle orbitals. The method is in principle
exact. We illustrate this method with a trapped atomic boson gas, where the
atoms interact via an attractive or repulsive contact two-body potential. We
choose as the single-particle basis a real-space grid. We compare with exact
results in small systems, and arbitrarily-sized systems of untrapped bosons
with attractive interactions in one dimension, where analytical solutions
exist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field
calculations for trapped atoms, and discuss the close formal relation between
our method and the GP approach. Our method provides a way to systematically
improve upon GP while using the same framework, capturing interaction and
correlation effects with a stochastic, coherent ensemble of non-interacting
solutions. We discuss various algorithmic issues, including importance sampling
and the back-propagation technique for computing observables, and illustrate
them with numerical studies. We show results for systems with up to N ~ 400
bosons.
