  We present a simple, general purpose, quantum Monte-Carlo algorithm for
out-of-equilibrium interacting nanoelectronics systems. It allows one to
systematically compute the expansion of any physical observable (such as
current or density) in powers of the electron-electron interaction coupling
constant $U$. It is based on the out-of-equilibrium Keldysh Green's function
formalism in real-time and corresponds to evaluating all the Feynman diagrams
to a given order $U^n$ (up to $n=15$ in the present work). A key idea is to
explicitly sum over the Keldysh indices in order to enforce the unitarity of
the time evolution. The method can easily reach long time, stationary regimes,
even at zero temperature. We then illustrate our approach with an application
to the Anderson model, an archetype interacting mesoscopic system. We recover
various results of the literature such as the spin susceptibility or the "Kondo
ridge" in the current-voltage characteristics. In this case, we found the
Monte-Carlo free of the sign problem even at zero temperature, in the
stationary regime and in absence of particle-hole symmetry. The main limitation
of the method is the lack of convergence of the expansion in $U$ for large $U$,
i.e. a mathematical property of the model rather than a limitation of the
Monte-Carlo algorithm. Standard extrapolation methods of divergent series can
be used to evaluate the series in the strong correlation regime.
