Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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We consider the relationship between computational complexity and the laws of physics, and show that nonlinear generalizations of quantum mechanics allow for polynomial-time solution of NP-complete and #P problems. Whether or not experiments ultimately reveal small nonlinearities in the evolution of quantum states (indeed, we believe that they most likely will not), these results underscore the close relationship between physics and computation.