Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems
Quantum Physics
2009-10-31 v1
Abstract
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.
Cite
@article{arxiv.quant-ph/9801041,
title = {Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems},
author = {Daniel S. Abrams and Seth Lloyd},
journal= {arXiv preprint arXiv:quant-ph/9801041},
year = {2009}
}
Comments
10 pages, no figures, submitted to Phys. Rev. Lett