  We review the calculation of the equation of state of pure neutron matter
using quantum Monte Carlo (QMC) methods. QMC algorithms permit the study of
many-body nuclear systems using realistic two- and three-body forces in a
nonperturbative framework. We present the results for the equation of state of
neutron matter, and focus on the role of three-neutron forces at supranuclear
density. We discuss the correlation between the symmetry energy, the neutron
star radius and the symmetry energy. We also combine QMC and theoretical models
of the three-nucleon interactions, and recent neutron star observations to
constrain the value of the symmetry energy and its density dependence.
