  A restricted path integral method is proposed to simulate a type of quantum
system or Hamiltonian called a sum of controlled few-fermions on a classical
computer using Monte Carlo without a numerical sign problem. Then a
universality is proven to assert that any bounded-error quantum polynomial time
(BQP) algorithm can be encoded into a sum of controlled few-fermions and
simulated efficiently using classical Monte Carlo. Therefore, BQP is precisely
the same as the class of bounded-error probabilistic polynomial time (BPP),
namely, BPP = BQP.
