methods have been developed in physics and chemistry literature for many-body quantum dynamics, which is a central challenge in theoretical understanding of quantum systems. While a complete literature review is beyond the scope, we discuss here some related works to our approach.

The methods proposed in the literature can be roughly categorized into two groups. One class of methods is based on an efficient representation of the relevant part of the Hilbert space of the many-body quantum system, such as the multi-configurational time-dependent Hartree (MCTDH) [@MeyerMantheCederbaum:1990], originally developed for the nucleus dynamics, which uses multi-configurational Hartree ansatz to represent wave functions. Other methods belong to this class include the time-evolving block decimation (TEBD) [@Vidal:2003] and the time-dependent density matrix renormalization group (tDMRG) [@Schollwock:2011] as extensions of the DMRG method [@White:1992] to dynamical problems. These methods are based on matrix product states and hence rather powerful for one (physical) dimensional systems, but face difficulty in extending to higher dimensions.

The other class of methods is based on Monte Carlo sampling. A particular relevant class of quantum Monte Carlo methods to our method is the continuous-time quantum Monte Carlo (CT-QMC) [@RubtsovSavkinLichtenstein:2005; @Prokofev:96; @Gull:2011], which can be understood as a continuum time limit 