色琼斯多项式的一种有效量子算法
An efficient quantum algorithm for colored Jones polynomials
摘要：
我们构造了一个量子算法来有效地逼近任何有向链路L在单位根q上的平面表示的有色琼斯多项式。我们的构造基于SU（2）Chern-Simons拓扑量子场论（以及相关的Wess-Zumino-Witten共形场论），并利用q-变形自旋网络作为计算背景。如在（S。Garnerone，A. Marzuoli，M. Rasetti，quant-ph/0601169），可以在多个基本步骤中评估有色琼斯多项式，从上到下由链接的交叉点的数量的线性函数限定，并且相对于链接链的数量多项式地限定。在这里，我们表明，考尔酉表示的彩色定向辫子，可以有效地近似在一个标准的量子线路。
英文摘要：
We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. Our construction is based on SU(2) Chern-Simons topological quantum field theory (and associated Wess-Zumino-Witten conformal field theory) and exploits the q-deformed spin network as computational background. As proved in (S. Garnerone, A. Marzuoli, M. Rasetti, quant-ph/0601169), the colored Jones polynomial can be evaluated in a number of elementary steps, bounded from above by a linear function of the number of crossings of the link, and polynomially bounded with respect to the number of link strands. Here we show that the Kaul unitary representation of colored oriented braids used there can be efficiently approximated on a standard quantum circuit.
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