科研之友
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摘要
The permanent of a square matrix is defined in a way similar to the determinant, but without using signs. The exact computation of the permanent is hard, but there are Monte Carlo algorithms that can estimate general permanents. Given a planar diagram of a link L with n crossings, we define a 7n x 7n matrix whose permanent equals the Jones polynomial of L. This result, accompanied with recent work of Freedman, Kitaev, Larsen and Wang (2003) [8], provides a Monte Carlo algorithm for any decision problem belonging to the class BQP, i.e. such that it can be computed with bounded error in polynomial time using quantum resources.
- 出版日期2011-10
