Non-Abelian statistics with mixed-boundary punctures on the toric code
Non-Abelian statistics with mixed-boundary punctures on the toric code
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DOI：
10.1103/physreva.105.042417
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发表时间：
2022-04-11
影响因子：
2.9
通讯作者：
Browne, Dan E.
中科院分区：
文献类型：
--
作者：
Benhemou, Asmae;Pachos, Jiannis K.;Browne, Dan E.
环码是拓扑序实现阿贝尔任意子的一个简单且精确可解的例子。然而，它被证明支持非局部晶格缺陷，即扭曲，表现出非阿贝尔任意行为[物理学]。科学通报，2009,(5):391 - 391。在这个结果的激励下，我们研究了在环面代码中从穿刺缺陷中获得非阿贝尔统计的可能性。我们证明了混合边界穿孔的编码再现了伊辛融合，并在其编织上再现了逻辑保利- x。我们的构造为局部晶格缺陷展现出可用于量子信息任务的非阿贝尔性质铺平了道路。
The toric code is a simple and exactly solvable example of topological order realizing Abelian anyons. However, it was shown to support nonlocal lattice defects, namely twists, which exhibit non-Abelian anyonic behavior [Phys. Rev. Lett. 105, 030403 (2010)]. Motivated by this result, we investigated the potential of having non-Abelian statistics from puncture defects on the toric code. We demonstrate that an encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli-X upon their braiding. Our construction paves the way for local lattice defects to exhibit non-Abelian properties that can be employed for quantum information tasks.