Ising拓扑量子计算机中辫子群的两个不等价旋量表示的计算等价性
Computational equivalence of the two inequivalent spinor representations of the braid group in the Ising topological quantum computer
摘要：
我们证明了在Pfidian拓扑量子计算机中描述2n+2个非Abel Ising任意子交换的辫群\B_{2n+2}的两个不等价旋量表示从计算的观点是等价的，即，在这两种情况下可以通过编织实现的拓扑保护的量子门的集合精确地重合。我们给出了2n+2伊辛任意子旋量表示中几乎所有辫子的显式矩阵，以及重要的递推关系。我们的详细分析使我们能够更好地理解这两种不等价表示之间的物理差异，并提出一个过程，可以确定任何具体物理实现的Pfiran量子计算机的表示类型。
英文摘要：
We demonstrate that the two inequivalent spinor representations of the braid group \B_{2n+2}, describing the exchanges of 2n+2 non-Abelian Ising anyons in the Pfaffian topological quantum computer, are equivalent from computational point of view, i.e., the sets of topologically protected quantum gates that could be implemented in both cases by braiding exactly coincide. We give the explicit matrices generating almost all braidings in the spinor representations of the 2n+2 Ising anyons, as well as important recurrence relations. Our detailed analysis allows us to understand better the physical difference between the two inequivalent representations and to propose a process that could determine the type of representation for any concrete physical realization of the Pfaffian quantum computer.
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