A scheme for demonstration of fractional statistics of anyons in an exactly solvable model

Abstract

We propose a scheme to demonstrate fractional statistics of anyons in an exactly solvable lattice model proposed by Kitaev that involves four-body interactions. The required many-body ground state, as well as the anyon excitations and their braiding operations, can be conveniently realized through \textit{dynamic}laser manipulation of cold atoms in an optical lattice. Due to the perfect localization of anyons in this model, we show that a quantum circuit with only six qubits is enough for demonstration of the basic braiding statistics of anyons. This opens up the immediate possibility of proof-of-principle experiments with trapped ions, photons, or nuclear magnetic resonance systems.

4 pages, 3 figures

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• Scalable multi-particle entanglement of trapped ions
• Experimental entanglement of six photons in graph states
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Cited by in corpus (57)

• Quantum Simulation
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• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Topological phases, Majorana modes and quench dynamics in a spin ladder system
• Anyonic interferometry and protected memories in atomic spin lattices
• Simulations of quantum double models
• Majorana edge modes in the Kitaev model
• Emulating anyonic fractional statistical behavior in a superconducting quantum circuit
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• Superconducting Quantum Simulator for Topological Order and the Toric Code
• Entanglement negativity and sudden death in the toric code at finite temperature
• Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
• Mermin inequalities for perfect correlations
• Experimental simulation of anyonic fractional statistics with an NMR quantum information processor
• Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
• Entanglement in eight-qubit graph states
• Transport in disordered monolayer molybdenum disulfide nanoflakes: evidence for inhomogeneous charge transport
• Generalized Ardehali-Bell inequalities for graph states
• Generalized Cluster States Based on Finite Groups
• Engineering Graph States of Atomic Ensembles by Photon-Mediated Entanglement
• Stroboscopic Generation of Topological Protection
• Topological wormholes
• Anyonic statistics with continuous variables
• Implementing topological quantum manipulation with superconducting circuits
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Detecting Topological Entanglement Entropy in a Lattice of Quantum Harmonic Oscillators
• Competing topological orders in three dimensions: X-cube versus toric code
• Engineering topological states and quantum-inspired information processing using classical circuits
• An Interferometry-Free Protocol for Demonstrating Topological Order
• Minimal instances for toric code ground states
• Realization of Topological Quantum Computation with surface codes
• Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds
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• Simulation of anyonic fractional statistics of Kitaev's toric model in circuit QED
• Measurement based Controlled Not gate for topological qubits in a Majorana fermion quantum-dot hybrid system
• Engineering the Kitaev spin liquid in a quantum dot system
• Simulation of non-Abelian Anyons using ribbon operators connected to a common base site
• Universal Quantum Computation with Continuous-Variable Abelian Anyons
• Fractional Excitations in Cold Atomic Gases
• Probing non-Abelian anyonic statistics with cold atoms in an optical lattice
• Implementing Genuine Multi-Qubit Entanglement of Two-Level-System Inside a Superconducting Phase Qubit
• Quasi-particle propagation in quantum Hall systems
• An anyon model in a toric honeycomb lattice
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• General scheme for preparation of different topological states on the cluster states
• Fracton and topological order in the XY checkerboard toric code
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• Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator
• Measuring the Unique Identifiers of Topological Order Based on Boundary-Bulk Duality and Anyon Condensation
• Permutation Phase and Gentile Statistics
• Anyonic two-photon statistics with a semiconductor chip