  We report the first successful application of the {\it ab initio} quantum
Monte Carlo (QMC) framework to a phonon dispersion calculation. A full phonon
dispersion of diamond is successfully calculated at the variational Monte Carlo
(VMC) level, based on the frozen-phonon technique. The VMC-phonon dispersion is
in good agreement with the experimental results, giving renormalized harmonic
optical frequencies very close to the experimental values, by significantly
improving upon density functional theory (DFT) in the generalized gradient
approximation. Key to success for the QMC approach is the statistical error
reduction in atomic force evaluation. We show that this can be achieved by
using well conditioned atomic basis sets, by explicitly removing the basis-set
redundancy, which reduces the statistical error of forces by up to two orders
of magnitude. This leads to affordable and accurate QMC-phonons calculations,
up to $10^{4}$ times more efficient than previous attempts, and paves the way
to new applications, particularly in correlated materials, where phonons have
been poorly reproduced so far.
