A linear-optical proof that the permanent is #P-hard
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Aaronson_A linear-optical.pdf
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177.79 KB
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Adobe PDF
Checksum (MD5)
a908bc20d7634880c4f1652086245c25
Author(s)
Aaronson, Scott
Date Issued
December 2011
Journal
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher
Royal Society, The
Citation
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.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1098/rspa.2011.0232
