  We present a quantum embedding methodology to resolve the Anderson impurity
model in the context of dynamical mean-field theory, based on an extended exact
diagonalization method. Our method provides a maximally localized quantum
impurity model, where the non-local components of the correlation potential
remain minimal. This method comes at a large benefit, as the environment used
in the quantum embedding approach is described by propagating correlated
electrons and hence offers a polynomial increase $O(N^4)$ of the number of
degrees of freedom for the embedding mapping without adding bath sites. We
report that quantum impurity models with as few as 3 bath sites can reproduce
both the Mott transition and the Kondo physics, thus opening a more accessible
route to the description of time-dependent phenomena. Finally, we obtain
excellent agreement for dynamical magnetic susceptibilities, poising this
approach as a candidate to describe 2-particle excitations such as excitons in
correlated systems. We expect that our approach will be highly beneficial for
the implementation of embedding algorithms on quantum computers, as it allows
for a fine description of the correlation in materials with a reduced number of
required qubits.
