论文标题
量子计算拓扑的角色品种和代数表面
Character varieties and algebraic surfaces for the topology of quantum computing
论文作者
论文摘要
结果表明，由于其$ sl_2（\ mathbb {c}）$ carture vartial的代表理论与代数表面有关。我们利用代数表面的Enriques-kodaira分类和相关的拓扑工具，以使这种表面明确。我们研究$ sl_2（\ mathbb {c}）$字符品种与拓扑量子计算（TQC）的连接，以替代Anyons的概念。 Hopf链接$ h $，其角色是Del Pezzo Surface $ F_H $（换向器的轨迹），是我们对TQC的看法的内核。 QUTRIT和两Q Qubit的魔术状态计算是从我们以前的工作中衍生出的Trefoil结的，可以从HOPF链接看作是TQC。某些两发者Bianchi组以及单数纤维的基本组$ \ tilde {e} _6 $和$ \ tilde {d} _4 $包含$ f_h $的角色。表面上等同于$ k_3 $表面的表面是其角色品种的另一种化合物。
It is shown that the representation theory of some finitely presented groups thanks to their $SL_2(\mathbb{C})$ character variety is related to algebraic surfaces. We make use of the Enriques-Kodaira classification of algebraic surfaces and the related topological tools to make such surfaces explicit. We study the connection of $SL_2(\mathbb{C})$ character varieties to topological quantum computing (TQC) as an alternative to the concept of anyons. The Hopf link $H$, whose character variety is a Del Pezzo surface $f_H$ (the trace of the commutator), is the kernel of our view of TQC. Qutrit and two-qubit magic state computing, derived from the trefoil knot in our previous work, may be seen as TQC from the Hopf link. The character variety of some two-generator Bianchi groups as well as that of the fundamental group for the singular fibers $\tilde{E}_6$ and $\tilde{D}_4$ contain $f_H$. A surface birationally equivalent to a $K_3$ surface is another compound of their character varieties.
