论文标题
拓扑量子计算是双曲线
Topological quantum computation is hyperbolic
论文作者
论文摘要
我们表明，基于对witten-reshetikhin-turaev tqft的评估的拓扑量子计算机始终可以安排，以便将一个计算的打结图是双曲线结的图表。这些图甚至可以安排以具有其他良好的属性，例如与最小交叉数量交替。此外，在着色对象的自编写指数中，还原在多项式统一。各种复杂性理论硬度有关结的计算，以结的计算。特别是，我们认为结的双曲线几何形状不太可能对拓扑量子计算有用。
We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant of knots can always be arranged so that the knot diagrams with which one computes are diagrams of hyperbolic knots. The diagrams can even be arranged to have additional nice properties, such as being alternating with minimal crossing number. Moreover, the reduction is polynomially uniform in the self-braiding exponent of the coloring object. Various complexity-theoretic hardness results regarding the calculation of quantum invariants of knots follow as corollaries. In particular, we argue that the hyperbolic geometry of knots is unlikely to be useful for topological quantum computation.
