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A Linear-Optical Proof that the Permanent is #P-Hard
Published 8 Sep 2011 in quant-ph and cs.CC | (1109.1674v1)
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.
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