  We address the possibility of performing numerical Monte Carlo simulations
for the thermodynamics of quantum dissipative systems. Dissipation is
considered within the Caldeira-Leggett formulation, which describes the system
in the path-integral formalism through the inclusion of an influence action
that is bilocal and quadratic in the system's coordinates. At a first sight the
usual direct approach of discretizing the path integral could seem feasible,
but complications arise when one tries to introduce a physically meaningful
dissipation kernel: in particular its imaginary-time dependence turns out to be
severely singular and difficult to evaluate analytically, in spite of the
simple expressions for its Matsubara components. We therefore propose to face
the numerical problem using Fourier path-integral Monte Carlo, that can be
formulated in two different ways: transforming the continuous paths and then
truncating the high Fourier components (with possible improvements upon the
truncation procedure), or performing the Fourier transformation upon the
discretized paths. The latter choice leads to a simpler formulation and allows
for a better control of the extrapolation to the limit of infinite Trotter
number. The method is implemented for a single nonlinear particle with Ohmic
dissipation and for a phi^4 chain with Drude-like dissipation.
