In this study, we simulated a quantum rotor model describing a Josephson junction array (JJA) in the phase representation at zero temperature in a perpendicular magnetic field [Formula: see text] (in units of [Formula: see text]) on a [Formula: see text] square lattice with spacing a for [Formula: see text]. The superconductor-insulator transition (SIT) is tuned by the ratio of charging energy to Josephson coupling, U/J. Abrupt drops in the magnetization values were observed in the bigger lattices at certain values of B and U/J caused by the formation of vortices. Increasing U/J at a fixed B field causes quantum vortex melting. The magnetization drops to zero around [Formula: see text] indicating SIT. For B = 0.1 the SIT occurs without an intermediate vortex state and the magnetization scales as [Formula: see text], whereas for B = 0.4 the scaling is [Formula: see text] during the vortex melting. For B between 0.1 and 0.4 the scaling is not clear. We used the diffusion Monte Carlo (DMC) method with a guiding wavefunction optimized using the variational Monte Carlo (VMC) method. The ground state energy is calculated easily in DMC and its error estimates were generally smaller than [Formula: see text], both with and without the guiding wavefunction. Quantities like magnetization and vorticity that do not commute with the Hamiltonian were calculated using an efficient forward walking algorithm. Their estimates are affected severely in absence of the guiding wavefunction. With the guiding wavefunction, errors for the magnetization were generally less than [Formula: see text] and going up to [Formula: see text] percent around the phase transition from the Meissner to the vortex state, and without the guiding wavefunction errors were generally higher than [Formula: see text] and going up to [Formula: see text] around the critical point.