Topological states and braiding statistics using quantum circuits

Abstract

Using superconducting quantum circuits, we propose an approach to construct a Kitaev lattice, i.e., an anisotropic spin model on a honeycomb lattice with three types of nearest-neighbor interactions. We study two particular cases to demonstrate topological states (i.e., the vortex and bond states) and show how the braiding statistics can be revealed. Our approach provides an experimentally realizable many-body system for demonstrating exotic properties of topological phases.

4 pages, 2 figures

References in corpus (17)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Charge insensitive qubit design derived from the Cooper pair box
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• A toolbox for lattice spin models with polar molecules
• Superconducting Circuits and Quantum Information
• An exact chiral spin liquid with non-Abelian anyons
• Low-decoherence flux qubit
• Superconducting Nanocircuits for Topologically Protected Qubits
• Mosaic spin models with topological order
• Creation and Manipulation of Anyons in the Kitaev Model
• Anyonic Braiding in Optical Lattices
• The Wavefunction of an Anyon
• Spectroscopy of superconducting charge qubits coupled by a Josephson inductance
• Topological quantum phase transition in an extended Kitaev spin model
• Implementing topological quantum manipulation with superconducting circuits
• Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

Cited by in corpus (67)

• Quantum Simulation
• Atomic physics and quantum optics using superconducting circuits
• Microwave photonics with superconducting quantum circuits
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Quantum optimization using variational algorithms on near-term quantum devices
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Topologically Protected Quantum State Transfer in a Chiral Spin Liquid
• Quantum bits with Josephson junctions
• Physical solutions of the Kitaev honeycomb model
• Exceptional Spin Liquids from Couplings to the Environment
• Characterization of topological states via dual multipartite entanglement
• Pair Density Waves in Superconducting Vortex Halos
• Kitaev honeycomb and other exotic spin models with polar molecules
• Topologically Protected Quantum Coherence in a Superatom
• Magnetic impurities in the honeycomb Kitaev model
• Superconducting Quantum Simulator for Topological Order and the Toric Code
• Floquet engineering in superconducting circuits: from arbitrary spin-spin interactions to the Kitaev honeycomb model
• Experimental simulation of anyonic fractional statistics with an NMR quantum information processor
• Digital-analog quantum simulation of generalized Dicke models with superconducting circuits
• Quantum spin liquid in the semiclassical regime
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
• Experimental implementation of adiabatic passage between different topological orders
• Majorana states in inhomogeneous spin ladders
• Coupling spin ensembles via superconducting flux qubits
• Fermionic Models with Superconducting Circuits
• Quantum coherence in a compass chain under an alternating magnetic field
• Quantum information approach to the quantum phase transition in the Kitaev honeycomb model
• Kitaev spin models from topological nanowire networks
• Spin-1 Kitaev model in one dimension
• Kitaev model and dimer coverings on the honeycomb lattice
• Manipulating unpaired Majorana fermions in a quantum spin chain
• Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains
• Quantum memory coupled to cavity modes
• Quantum correlations and entanglement in a Kitaev-type spin chain
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• Analytical solutions of basic models in quantum optics
• Topological quantum error correction in the Kitaev honeycomb model
• Fate of Dirac Points in a Vortex Superlattice
• Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits
• Beyond adiabatic elimination: Effective Hamiltonians and singular perturbation
• Realization of the Exactly Solvable Kitaev Honeycomb Lattice Model in a Spin Rotation Invariant System
• Two-Magnon Bound States in the Kitaev Model in a $[111]$-Field
• Exact zero modes in a quantum compass chain under inhomogeneous transverse fields
• Fractionalized Prethermalization in a Driven Quantum Spin Liquid
• Stationary entanglement in strongly coupled qubits
• Compass and Kitaev models -- Theory and Physical Motivations
• Counterdiabatic route for preparation of state with long-range topological order
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• Periodic driving induced helical Floquet channels with ultracold atoms in momentum space
• Quantum statistics of the collective excitations of an atomic ensemble inside a cavity
• A continuum of compass spin models on the honeycomb lattice
• Block entropy for Kitaev-type spin chains in a transverse field
• Topological transitions in dissipatively coupled Su-Schrieffer-Heeger models
• Simulation of anyonic fractional statistics of Kitaev's toric model in circuit QED
• Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders
• Strongly-coupled Josephson junction array for simulation of frustrated one-dimensional spin models
• Probing non-Abelian anyonic statistics with cold atoms in an optical lattice
• Topological aspects of an exactly solvable spin chain
• Long-range Ising spins models emerging from frustrated Josephson junctions arrays with topological constraints
• Dynamical topological quantum computation using spin pulse control in the Heisenberg model
• Measuring Holographic Entanglement Entropy on a Quantum Simulator
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Simulation of the Majorana equation in circuit QED
• Quantum computation at the edge of a disordered Kitaev honeycomb lattice
• Edge states in quantum spin chains: the interplay among interaction, gradient magnetic field and Floquet engineering
• Digital Quantum Simulation of the Kitaev Quantum Spin Liquid
• Manipulating Edge Majorana Fermions in Vortex State