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

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

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 dif...

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Bibliographic Details
Main Author: Aaronson, Scott (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
Format: Article
Language:English
Published: Royal Society, The, 2012-08-09T14:47:58Z.
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Summary: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.
National Science Foundation (U.S.) (grant 0844626)
United States. Defense Advanced Research Projects Agency (YFA grant)

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