Ds. Abrams et S. Lloyd, NONLINEAR QUANTUM-MECHANICS IMPLIES POLYNOMIAL-TIME SOLUTION FOR NP-COMPLETE AND NUMBER-P PROBLEMS, Physical review letters, 81(18), 1998, pp. 3992-3995
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].