Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems

Details Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems

1998-01-21

arxiv.org/abs/quant-ph/9801041v1

Phys.Rev.Lett. 81 (1998) 3992-3995

Physics

Quantum Physics

10 pages, no figures, submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.81.3992

If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demonstrated using the Weinberg model of nonlinear quantum mechanics.

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