Lattice Monte Carlo evaluation of systems with non-real action (e.g. systems with non-zero chemical potential) results in exponentially large simulation time, which prevents the practical use of the method.
This is the sign problem.

We propose to address this problem, in the case of bose gas with chemical potential, by deforming the integration contour in the complex plane. We identify contours which are sign problem free up to relatively large lattice size. Moreover, the simulation time for these contours is linear with respect to the lattice size.