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A topological order is a new quantum phase that is beyond Landau'ssymmetry-breaking paradigm. Its defining features include robust degenerateground states, long-range entanglement and anyons. It was known that $R$- and$F$-matrices, which characterize the fusion-braiding properties of anyons, canbe used to uniquely identify topological order. In this article, we explore anessential question: how can the $R$- and $F$-matrices be experimentallymeasured? By using quantum simulations based on a toric code model withboundaries and state-of-the-art technology, we show that the braidings, i.e.the $R$-matrices, can be completely determined by the half braidings ofboundary excitations due to the boundary-bulk duality and the anyoncondensation. The $F$-matrices can also be measured in a scattering quantumcircuit involving the fusion of three anyons in two different orders. Thus weprovide an experimental protocol for measuring the unique identifiers oftopological order.

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