  An efficient continuous-time path-integral Quantum Monte Carlo algorithm for
the lattice polaron is presented. It is based on Feynman's integration of
phonons and subsequent simulation of the resulting single-particle
self-interacting system. The method is free from the finite-size and
finite-time-step errors and works in any dimensionality and for any range of
electron-phonon interaction. The ground-state energy and effective mass of the
polaron are calculated for several models. The polaron spectrum can be measured
directly by Monte Carlo, which is of general interest.
