  We present a quantum impurity solver based on a pseudo-particle framework,
which combines diagrammatic resummations for a three-point vertex with
diagrammatic Monte Carlo sampling of a four-point vertex. This recently
proposed approach [A. J. Kim et al., arXiv:2112.15549] is generalized here to
fermionic impurity problems and we discuss the technical details of the
implementation, including the time-stepping approach, the Monte Carlo updates,
and the routines for checking the two-particle irreducibility of the four-point
vertex. We also explain how the vertex information can be efficiently stored
using a Dubiner basis representation. The convergence properties of the
algorithm are demonstrated with applications to exactly solvable impurity
models and dynamical mean field theory simulations of the single-orbital
Hubbard model. It is furthermore shown that the algorithm can handle a
two-orbital problem with off-diagonal hybridizations, which would cause a
severe sign problem in standard hybridization-expansion Monte Carlo
simulations. Since the vertex-based algorithm successfully handles sign
oscillating integrals in equilibrium and samples only connected diagrams, it
may be a promising approach for real-time simulations.
