Topological Quantum Computation is Hyperbolic

被引：0

作者：

Samperton, Eric ^{[1
]}

机构：

[1] Purdue Univ, Dept Math & Comp Sci, 150 N Univ St, W Lafayette, IN 47907 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 402卷 / 01期

基金：

美国国家科学基金会;

关键词：

JONES POLYNOMIALS; CLASSICAL CONJECTURES; COMPLEXITY CLASSES; KNOT; CLASSIFICATION; DISTANCE; SURFACES; VOLUME;

D O I：

10.1007/s00220-023-04713-w

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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.

引用

页码：79 / 96

页数：18

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