  We present a strategy for mapping the dynamics of a fermionic quantum system
to a set of classical dynamical variables. The approach is based on imposing
the correspondence relation between the commutator and the Poisson bracket,
preserving Heisenberg's equation of motion for one-body operators. In order to
accommodate the effect of two-body terms, we further impose quantization on the
spin-dependent occupation numbers in the classical equations of motion, with a
parameter that is determined self-consistently. Expectation values for
observables are taken with respect to an initial quasiclassical distribution
that respects the original quantization of the occupation numbers. The proposed
classical map becomes complete under the evolution of quadratic Hamiltonians
and is extended for all even order observables. We show that the map provides
an accurate description of the dynamics for an interacting quantum impurity
model in the coulomb blockade regime, at both low and high temperatures. The
numerical results are aided by a novel importance sampling scheme that employs
a reference system to reduce significantly the sampling effort required to
converge the classical calculations.
