of the Trotter splitting based Hirsch-Fye QMC method [@HirschFye:1986]. While the CT-QMC method was originally developed for imaginary time propagation, it has also been extended to real time dynamics in recent years [@MuhlbacherRabani:2008; @CohenGullReichmanMillis:2015], in particular for impurity models in condensed matter physics. Another related quantum Monte Carlo method is the auxiliary field quantum Monte Carlo [@ZhangKrakauer:2003; @Zhang:2013] based on the Hubbard-Stratonovich transformation [@Hubbard:1959; @Stratonovich:1958], which represents the imaginary time evolution of the many-body electronic wave function as a stochastic sum of Slater determinants. We also note a different strategy – discrete truncated Wigner approximation (DTWA) – proposed recently [@Schachenmayer:2015] based on a tensor product ansatz on the level of discrete Wigner representation of many-body spin density matrix. The Monte Carlo method is used to sample initial states according to the phase space distribution.

Our method can be understood at the interface of the above two categories: The idea of series expansion is also utilized in the CT-QMC method. Unlike CT-QMC, which resorts to diagrammatic perturbation ideas in many-body theory, our stochastic evaluation method is based on ansatz representation similar to those used in MCTDH. The proposed method is not restricted to a particular geometry of the systems, and is 