A linear-optical proof that the permanent is #P-hard

S. Aaronson
2011 Proceedings of the Royal Society A  
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.
doi:10.1098/rspa.2011.0232 fatcat:ir24v7roubbirld4ten7nydvua