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We present a simple, general purpose, quantum Monte-Carlo algorithm forout-of-equilibrium interacting nanoelectronics systems. It allows one tosystematically compute the expansion of any physical observable (such ascurrent or density) in powers of the electron-electron interaction couplingconstant $U$. It is based on the out-of-equilibrium Keldysh Green's functionformalism in real-time and corresponds to evaluating all the Feynman diagramsto a given order $U^n$ (up to $n=15$ in the present work). A key idea is toexplicitly sum over the Keldysh indices in order to enforce the unitarity ofthe time evolution. The method can easily reach long time, stationary regimes,even at zero temperature. We then illustrate our approach with an applicationto the Anderson model, an archetype interacting mesoscopic system. We recovervarious results of the literature such as the spin susceptibility or the "Kondoridge" in the current-voltage characteristics. In this case, we found theMonte-Carlo free of the sign problem even at zero temperature, in thestationary regime and in absence of particle-hole symmetry. The main limitationof 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 theMonte-Carlo algorithm. Standard extrapolation methods of divergent series canbe used to evaluate the series in the strong correlation regime.

Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices