Quantum automata, braid group and link polynomials
Quantum automata, braid group and link polynomials
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量子自动机、编织群和链接多项式
DOI：
10.26421/qic7.5-6-5
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
M. Rasetti
中科院分区：
文献类型：
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作者：
S. Garnerone;A. Marzuoli;M. Rasetti
自旋网络量子模拟器模型本质上对（量子变形的）SU（2）Rachah-Wigner张量代数进行编码，特别适合解决低维拓扑和群论中出现的问题。在这个组合框架中，我们实现家庭的有限状态和离散时间的量子自动机能够接受的语言所产生的辫子群，其过渡幅度是有色琼斯多项式。的多项式的自动机计算（的平台封闭）的链接L上的2N股在任何固定的单位根被示出为有界的从上面的线性函数的交叉的链接的数量，一方面，和多项式有界的编织指数2N，另一方面。时间复杂度函数关于单位根q中出现的整数k的增长率可以通过求助于由Chern-Simons理论给出的场论背景来估计为（多项式）有界。
The spin-network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah-Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this combinatorial framework we implement families of finite-states and discrete-time quantum automata capable of accepting the language generated by the braid group, and whose transition amplitudes are colored Jones polynomials. The automaton calculation of the polynomial of (the plat closure of) a link L on 2N strands at any fixed root of unity is shown to be bounded from above by a linear function of the number of crossings of the link, on the one hand, and polynomially bounded in terms of the braid index 2N, on the other. The growth rate of the time complexity function in terms of the integer k appearing in the root of unity q can be estimated to be (polynomially) bounded by resorting to the field theoretical background given by the Chern-Simons theory.
关于结和 3 流形不变量的问题
DOI：
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发表时间：
2004
期刊：
Invariants of knots and 3-manifolds (Kyoto 2001), Geom.Topol.Monogr. (Geom.Topol.Publ.Coventry, 2004) 4
影响因子：
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作者：
K.Mikami;T.Mizutani;T.Ohtsuki (ed.)
通讯作者：
T.Ohtsuki (ed.)