  We extend the recently developed Quantum Quasi-Monte Carlo (QQMC) approach to
obtain the full frequency dependence of Green functions in a single
calculation. QQMC is a general approach for calculating high-order perturbative
expansions in power of the electron-electron interaction strength. In contrast
to conventional Markov chain Monte Carlo sampling, QQMC uses low-discrepancy
sequences for a more uniform sampling of the multi-dimensional integrals
involved and can potentially outperform Monte Carlo by several orders of
magnitudes. A core concept of QQMC is the a priori construction of a "model
function" that approximates the integrand and is used to optimize the sampling
distribution. In this paper, we show that the model function concept extends to
a kernel approach for the computation of Green functions. We illustrate the
approach on the Anderson impurity model and show that the scaling of the error
with the number of integrand evaluations $N$ is $\sim 1/N^{0.86}$ in the best
cases, and comparable to Monte Carlo scaling $\sim 1/N^{0.5}$ in the worst
cases. We find a systematic improvement over Monte Carlo sampling by at least
two orders of magnitude while using a basic form of model function. Finally, we
compare QQMC results with calculations performed with the Fork Tensor Product
State (FTPS) method, a recently developed tensor network approach for solving
impurity problems. Applying a simple Pad\'e approximant for the series
resummation, we find that QQMC matches the FTPS results beyond the perturbative
regime.
