Iulianelli Filippo, Kim Sung, Sussan Joshua, Lauda Aaron D
Department of Physics, University of Southern California, Los Angeles, CA, USA.
Department of Mathematics, University of Southern California, Los Angeles, CA, USA.
Nat Commun. 2025 Aug 5;16(1):6408. doi: 10.1038/s41467-025-61342-8.
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2 + 1 dimensions. These enhanced theories offer more powerful models for quantum computation. The conventional theory of Ising anyons, which is believed to describe excitations in the ν = 5/2 fractional quantum Hall state, is not universal for quantum computation via braiding of quasiparticles. However, we show that the non-semisimple theory introduces new anyon types that extend the Ising framework. By adding just one new anyon type, universal quantum computation can be achieved through braiding alone. This result opens new avenues for realizing fault-tolerant quantum computing in topologically ordered systems.
我们提出了一个用于拓扑量子计算的框架，该框架使用了新发现的2 + 1维拓扑量子场论的非半单类似物。这些增强理论为量子计算提供了更强大的模型。传统的伊辛任意子理论被认为可以描述ν = 5/2分数量子霍尔态中的激发，但它对于通过准粒子编织进行量子计算并不具有通用性。然而，我们表明非半单理论引入了扩展伊辛框架的新任意子类型。仅通过添加一种新的任意子类型，就可以仅通过编织实现通用量子计算。这一结果为在拓扑有序系统中实现容错量子计算开辟了新途径。
