  Monte Carlo studies involving real time dynamics are severely restricted by
the sign problem that emerges from highly oscillatory phase of the path
integral. In this letter, we present a new method to compute real time
quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo
simulations. The key idea is to deform the path integration domain to a complex
manifold where the phase oscillations are mild and the sign problem is
manageable. We use the previously introduced "contraction algorithm" to create
a Markov chain on this alternative manifold. We substantiate our approach by
analyzing the quantum mechanical anharmonic oscillator. Our results are in
agreement with the exact ones obtained by diagonalization of the Hamiltonian.
The method we introduce is generic and in principle applicable to quantum field
theory albeit very slow. We discuss some possible improvements that should
speed up the algorithm.
