Quantum Computing, NPcomplete Problems and Chaotic Dynamics
Abstract
An approach to the solution of NPcomplete 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 HartreeFock 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.
 Publication:

arXiv eprints
 Pub Date:
 December 1999
 arXiv:
 arXiv:quantph/9912100
 Bibcode:
 1999quant.ph.12100O
 Keywords:

 Quantum Physics;
 Chaotic Dynamics;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Computer Science  Computational Complexity;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Atomic Physics
 EPrint:
 11 pages, 1 figure