  Current nonequilibrium Monte Carlo methods suffer from a dynamical sign
problem that makes simulating real-time dynamics for long times exponentially
hard. We propose a new `Inchworm Algorithm', based on iteratively reusing
information obtained in previous steps to extend the propagation to longer
times. The algorithm largely overcomes the dynamical sign problem, changing the
scaling from exponential to quadratic. We use the method to solve the Anderson
impurity model in the Kondo and mixed valence regimes, obtaining results both
for quenches and for spin dynamics in the presence of an oscillatory magnetic
field.
