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"Universal Quantum Computation with Gapped Boundaries", Iris Cong, Meng Cheng, Zhenghan Wang, 2017

Reviewed August 18, 2023

Citation: Cong, Iris, Meng Cheng, and Zhenghan Wang. "Universal quantum computation with gapped boundaries." Physical Review Letters 119.17 (2017): 170504.

Web: https://arxiv.org/abs/1707.05490

Tags: Abelian-anyons, Quantum-hall-effect, Defects/boundaries, Universal-scheme

T his paper shows that a version of topological quantum field theory with boundary can give universal quantum computation, even with abelian anyons. This is motivated by recent fractional quantum Hall experiments, which demonstrate that certain systems have "gapped boundaries" in additional to just a a gapped bulk. The anyons in these gapped boundaries have non-abelian properties, even if the bulk is abelian. In particular, at the simplest fractional filling of the quantum Hall experiment v=1/3 you get a universal model.

The bulk anyons at v=1/3 are Z3 anyons, and the boundary gives extra power via the so-called "topological charge measurement" primitive. The popular summary of this article could be: "well-tuned boundaries give large computational power in topological systems". It is not clear if this power can extend to error correcting codes, though that is in some sense irrelevant because Zhenghan's goal with this paper is to make a true topological quantum computer.