  An approach to the solution of NP-complete problems based on quantum
computing and chaotic dynamics is proposed. We consider the satisfiability
problem and argue that the problem, in principle, can be solved in polynomial
time if we combine the quantum computer with the chaotic dynamics amplifier
based on the logistic map. We discuss a possible implementation of such a
chaotic quantum computation by using the atomic quantum computer with quantum
gates described by the Hartree-Fock equations. In this case, in principle, one
can build not only standard linear quantum gates but also nonlinear gates and
moreover they obey to Fermi statistics. This new type of entaglement related
with Fermi statistics can be interesting also for quantum communication theory.
