A Linear-Optical Proof that the Permanent is #P-Hard

Details A Linear-Optical Proof that the Permanent is #P-Hard A Linear-Optical Proof that the Permanent is #P-Hard

2011-09-08

arxiv.org/abs/1109.1674v1

Physics

Quantum Physics

12 pages, 2 figures, to appear in Proceedings of the Royal Society A. doi: 10.1098/rspa.2011.0232

Scientific paper

One of the crown jewels of complexity theory is Valiant's 1979 theorem that
computing the permanent of an n*n matrix is #P-hard. Here we show that, by
using the model of linear-optical quantum computing---and in particular, a
universality theorem due to Knill, Laflamme, and Milburn---one can give a
different and arguably more intuitive proof of this theorem.

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