NONLINEAR QUANTUM-MECHANICS IMPLIES POLYNOMIAL-TIME SOLUTION FOR NP-COMPLETE AND NUMBER-P PROBLEMS

If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete and #P problem s in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. Using the Weinberg model as a simple example, the explicit construction of these gates is derived from the underlying physics. Nonlinear quantum algorithms are also presented using Polchinski type nonlinearities whi ch do not allow for superluminal communication. [S0031 -9007(98)07489- 4].