# A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo

## TL;DR

This paper introduces a hybrid method combining selected configuration interaction (SCI) with initiator full configuration interaction quantum Monte Carlo (i-FCIQMC), enabling larger sampled spaces and improved energy estimates while managing computational costs.

## Contribution

The authors propose a novel approach that uses SCI-selected spaces as initiators in i-FCIQMC, allowing larger spaces and variational calculations, improving accuracy over traditional methods.

## Key findings

- Larger initiator spaces are feasible with manageable population plateaus.
- The method yields more accurate energies compared to standard i-FCIQMC.
- It offers a complementary approach to SCI+PT2 with potential for better accuracy and efficiency.

## Abstract

We present an approach to combining selected configuration interaction (SCI) and initiator full configuration interaction quantum Monte Carlo (i-FCIQMC). In the current i-FCIQMC scheme, the space of initiators is chosen dynamically by a population threshold. Here, we instead choose initiators as the selected space (V) from a prior SCI calculation, allowing substantially larger initiator spaces for a given walker population. While SCI+PT2 adds a perturbative correction in the first-order interacting space (FOIS) beyond V, the approach presented here allows a variational calculation in the same space, and a perturbative correction in the second-order interacting space. The use of a fixed initiator space reintroduces population plateaus into FCIQMC, but it is shown that the plateau height is typically only a small multiple of the size of V. Thus, for a comparable fundamental memory cost to SCI+PT2, a substantially larger space can be sampled. The resulting method can be seen as a complementary approach to SCI+PT2, which is more accurate but slower for a common selected/initiator space. More generally, our results show that approaches exist to significantly improve initiator energies in i-FCIQMC, while still ameliorating the fermion sign problem relative to the original FCIQMC method.