As a proof of concept, calculations were performed in linear H 8 using the STO-3G basis set, with the type of BE being BE2. The meaning of n in BEn in terms of fragment partition means that in addition to the central atom, other atoms that are in the (n -1)-th coordination shell are also included in a fragment. Therefore, with respect to partitioning a chain like molecule via BE2, each fragment always contains three atoms, including the central atom and the two nearest neighbours around this atom. A more detailed description of the partitioning scheme for arbitrary systems can be found in relevant literature. Figure below shows the structure of linear H 8 and how the molecule is partitioned via BE2. Since bath orbitals are also involved in the embedding process, there are 6 orbitals and 6 electrons (instead of 3) in each BE equation that needs to be solved, the Hilbert space of the embedding fragment is 400 Slater determinants. Intrinsic Atomic Orbitals (IAO) are used as the LOs in the fragments. The Schmidt decomposition of the molecular wavefunction and the partitioning of the fragments were performed using in-house code, while NECI was interfaced and used to solve the BE equations stochastically. More simulation details, including how the integrals are generated and how the 1-and 2-PDMs are sampled, are available in the Supporting Information and relevant literature. In addition, the initiator approximation is used to speed up the calculation, making the solver i-FCIQMC, and for every BE-i-FCIQMC calculation, all the determinants up to doubles are allowed to propagate deterministically to reduce the stochastic error. It can be seen that there is a sharp decrease in the minimum matching error, which can be explained from the increase of the granularity of the i-FCIQMC wavefunction as the number of walkers increases. The thresholds of the matching error to converge a calculation are therefore set to be 2.0 × 10 -3 , 8.0 × 10 -4 , 5.0 × 10 -4 , 2.5 × 10 -4 and 2.0 × 10 -4 respectively for five different numbers of walkers. Figure shows the proportion of the average correlation energy recovered from 6 parallel calculations relative to a deterministic BE-FCI, in which the convergence threshold is set to be 1 × 10 -6 . It is worth noticing that before the stochastic noise significantly affects the matching error, i.e., at a similar order of magnitude, the number of iterations needed to converge the BE-FCI and BE-i-FCIQMC to a designated matching error is similar. According to the figure, it can be deduced that the quality of the calculation is improved by increasing the number of walkers as the recovered correlation energy is closer to 100% and the stochastic error decreases. Both of these observations are similarly results of an increase in the granularity of the wavefunction with the number of walkers. It should be expected that this phenomenon is universal regardless of the chemical system, since the deviation in the values from the FCIQMC density matrix to the FCI density matrix should be zero in the large walker limit.