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

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.

arXiv comment12 pages, 6 figures, 1 table

References in corpus (15)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Zoo of quantum-topological phases of matter
• Identifying Topological Order by Entanglement Entropy
• Quantum orders in an exact soluble model
• Classification of Topological Defects in Abelian Topological States
• A scheme for demonstration of fractional statistics of anyons in an exactly solvable model
• Boundary-bulk relation in topological orders
• A mathematical theory of gapless edges of 2d topological orders. Part I
• Universal Quantum Computation with Gapped Boundaries
• Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
• Experimentally Probing Topological Order and Its Breakdown via Modular Matrices