Measuring the Unique Identifiers of Topological Order Based on Boundary-Bulk Duality and Anyon Condensation

• URL: http://arxiv.org/abs/2005.03236v4
• Date: Tue, 22 Dec 2020 15:55:02 GMT
• Title: Measuring the Unique Identifiers of Topological Order Based on Boundary-Bulk Duality and Anyon Condensation
• Authors: Yong-Ju Hai, Ze Zhang, Hao Zheng, Liang Kong, Jiansheng Wu, Dapeng Yu
• Abstract summary: A topological order is a new quantum phase beyond Landau's symmetry-breaking paradigm. It is known that $R$- and $F$-matrices, which characterize the fusion-braiding properties of anyons, can be used to identify topological order. We show that the braidings can be completely determined by the half braidings of boundary excitations. The $F$-matrices can also be measured in a scattering quantum circuit involving the fusion of three anyons in two different orders.
• Score: 6.191686890868695
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A topological order is a new quantum phase that is beyond Landau's symmetry-breaking paradigm. Its defining features include robust degenerate ground states, long-range entanglement and anyons. It was known that $R$- and $F$-matrices, which characterize the fusion-braiding properties of anyons, can be used to uniquely identify topological order. In this article, we explore an essential question: how can the $R$- and $F$-matrices be experimentally measured? By using quantum simulations based on a toric code model with boundaries and state-of-the-art technology, we show that the braidings, i.e. the $R$-matrices, can be completely determined by the half braidings of boundary excitations due to the boundary-bulk duality and the anyon condensation. The $F$-matrices can also be measured in a scattering quantum circuit involving the fusion of three anyons in two different orders. Thus we provide an experimental protocol for measuring the unique identifiers of topological order.

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