The Jones polynomial: quantum algorithms and applications in quantum complexity theory
نویسندگان
چکیده
منابع مشابه
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
We analyze relationships between the Jones polynomial and quantum computation. First, we present two polynomial-time quantum algorithms which give additive approximations of the Jones polynomial, in the sense of Bordewich, Freedman, Lovász and Welsh, of any link obtained from a certain general family of closures of braids, evaluated at any primitive root of unity. This family encompasses the we...
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It is shown that 2 + 1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized from S to arbitrary three manifolds, giving invariants of three manifolds that are compu...
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In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form e. This description is given with two objectives in mind. The first is to describe the algorithm in such a way as to make explicit the underlying and inherent control structure. The second is to make this alg...
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ژورنال
عنوان ژورنال: Quantum Information and Computation
سال: 2008
ISSN: 1533-7146,1533-7146
DOI: 10.26421/qic8.1-2-10