Fast algorithms of bath calculations in simulations of quantum system-bath dynamics

We present fast algorithms for the summation of Dyson series and inchworm Monte Carlo method quantum systems that are coupled with harmonic baths. The based on evolving integro-differential equations where most expensive part comes from computation bath influence functionals. To accelerate computation, we design reusing functionals computed in previous time steps to reduce number calculations. It is proven proposed such calculations by a factor O(N), N total steps. Numerical experiments carried out show efficiency verify theoretical results.