Before revision:  Assuming R < 1, where R is a parameter characterizing the ratio of the nonlinearity to the linear dissipation, this algorithm has complexity T^2poly(\log T, \log n  )/\epsilon, where T is the evolution time and \epsilon is the allowed error in the output quantum state.
After revision:  Assuming R < 1, where R is a parameter characterizing the ratio of the nonlinearity to the linear dissipation, this algorithm has complexity T^2poly(\log T, \log n , \log 1/\epsilon )/\epsilon, where T is the evolution time and \epsilon is the allowed error in the output quantum state.