A Linear-Optical Proof that the Permanent is #P-Hard
arXiv:1109.1674 · doi:10.1098/rspa.2011.0232
Abstract
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.
12 pages, 2 figures, to appear in Proceedings of the Royal Society A. doi: 10.1098/rspa.2011.0232