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Nonlinear Quantum Mechanics Implies Polynomial-Time Solution for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">NP</mml:mi></mml:math>-Complete and #<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">P</mml:mi></mml:math>Problems
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve $\mathrm{NP}$-complete and # $P$ problems in polynomial time. We provide algorithms that solve $\mathrm{NP}$-complete and # $P$ oracle problems by exploiting nonlinear quantum logic gates. Using the Weinberg model as a simple example, …