  We explore two complementary modifications of the hybridization-expansion
continuous-time Monte Carlo method, aiming at large multi-orbital quantum
impurity problems. One idea is to compute the imaginary-time propagation using
a matrix product states representation. We show that bond dimensions
considerably smaller than the dimension of the Hilbert space are sufficient to
obtain accurate results, and that this approach scales polynomially, rather
than exponentially with the number of orbitals. Based on scaling analyses, we
conclude that a matrix product state implementation will outperform the
exact-diagonalization based method for quantum impurity problems with more than
12 orbitals. The second idea is an improved Monte Carlo sampling scheme which
is applicable to all variants of the hybridization expansion method. We show
that this so-called sliding window sampling scheme speeds up the simulation by
at least an order of magnitude for a broad range of model parameters, with the
largest improvements at low temperature.
