  The amplitude (Higgs) mode is a ubiquitous collective excitation related to
spontaneous breaking of a continuous symmetry. We combine quantum Monte Carlo
(QMC) simulations with stochastic analytic continuation to investigate the
dynamics of the amplitude mode in a three-dimensional dimerized quantum spin
system. We characterize this mode by calculating the spin and dimer spectral
functions near the quantum critical point, finding that both the energies and
the intrinsic widths satisfy field-theoretical scaling predictions. While the
line width of the spin response is close to that observed in neutron scattering
experiments on TlCuCl$_3$, the dimer response is significantly broader. Our
results demonstrate that highly non-trivial dynamical properties are accessible
by modern QMC and analytic continuation methods.
