Simulation of non-Abelian Anyons using ribbon operators connected to a common base site

Abstract

A convenient and effective way in the quantum double model to study anyons in a topological space with a tensor product structure is to create and braid anyons using ribbon operators connected to a common base site [A. Kitaev Ann.\ Phys. (N.Y.) \textbf{303}, 2 (2003)]. We show how this scheme can be simulated in a physical system by constructing long ribbon operators connected to a base site that is placed faraway. We describe how to move and braid anyons using these ribbon operators, and how to perform measurement on them. We also give the smallest scale of a system that is sufficient for proof-of-principle demonstration of our scheme.

16 pages

References in corpus (9)

• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Simulations of quantum double models
• Anyonic Braiding in Optical Lattices
• The Wavefunction of an Anyon
• Integrated photonic qubit quantum computing on a superconducting chip
• Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator

Cited by in corpus (5)

• Universal quantum computation in the surface code using non-Abelian islands
• Exactly soluble lattice models for non-abelian states of matter in 2 dimensions
• Quantum double aspects of surface code models
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Spin chains, defects, and quantum wires for the quantum-double edge