  A continuous-time path integral Quantum Monte Carlo method using the
directed-loop algorithm is developed to simulate the Anderson single-impurity
model in the occupation number basis. Although the method suffers from a sign
problem at low temperatures, the new algorithm has many advantages over
conventional algorithms. For example, the model can be easily simulated in the
Kondo limit without time discretization errors. Further, many observables
including the impurity susceptibility and a variety of fermionic observables
can be calculated efficiently. Finally the new approach allows us to explore a
general technique, called the multi-level algorithm, to solve the sign problem.
We find that the multi-level algorithm is able to generate an exponentially
large number of configurations with an effort that grows as a polynomial in
inverse temperature such that configurations with a positive sign dominate over
those with negative signs. Our algorithm can be easily generalized to other
multi-impurity problems.
