拓扑量子计算是双曲的
Topological quantum computation is hyperbolic
AI总结：
该研究证明基于Witten-Reshetikhin-Turaev TQFT纽结不变量的拓扑量子计算可配置为使用双曲纽结图，归约具多项式一致性，得出纽结量子不变量计算的难度推论，指出双曲几何难用于拓扑量子计算。
摘要：
我们证明，基于对纽结的Witten-Reshetikhin-Turaev TQFT（拓扑量子场论）不变量求值的拓扑量子计算机，总能被配置为使其计算所用的纽结图是双曲纽结的图。这些图甚至可被设置为具备额外优良性质，例如为具有最小交叉数的交错纽结图。此外，该归约在着色对象的自辫指数上具有多项式一致性。关于纽结量子不变量计算的多种复杂性理论难度结果可作为推论得出。特别是，我们认为纽结的双曲几何不太可能对拓扑量子计算有用。
英文摘要：
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.
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