A linear-optical proof that the permanent is #P-hard
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One of the crown jewels of complexity theory is Valiant's 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 owing to Knill, Laflamme and Milburn—one can give a different and arguably more intuitive proof of this theorem.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
Royal Society, The
Aaronson, S. “A linear-optical proof that the permanent is #P-hard.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467.2136 (2011): 3393-3405.
Author's final manuscript