Braiding of non-Abelian anyons using pairwise interactions

Abstract

The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange (braiding) operators of anyons by adiabatically varying pairwise interactions between them rather than their positions. We analyze a system composed by four anyons whose couplings define a T-junction and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains in order to recover the topological protection.

8 pages, 7 figures. Errors corrected, clarifications and comments added

References in corpus (43)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Rapidly Rotating Atomic Gases
• Interacting anyons in topological quantum liquids: The golden chain
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Measurement-Only Topological Quantum Computation
• Genons, twist defects, and projective non-Abelian braiding statistics
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices
• Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires
• Fractional topological superconductors with fractionalized Majorana fermions
• Interferometry of non-Abelian Anyons
• The non-Abelian Interferometer
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Non-adiabatic Effects in the Braiding of Non-Abelian Anyons in Topological Superconductors
• Measurement-Only Topological Quantum Computation via Anyonic Interferometry
• Collective states of interacting Fibonacci anyons
• Synthetic Topological Degeneracy by Anyon Condensation
• Microscopic models of interacting Yang-Lee anyons
• Splitting the Topological Degeneracy of non-Abelian Anyons
• Telegraph noise and the Fabry-Perot quantum Hall interferometer
• Bulk-edge coupling in the non-abelian $\nu =5/2$ quantum Hall interferometer
• Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
• Odd-Even Crossover in a non-Abelian $\nu =5/2$ Interferometer
• Quantum spin ladders of non-Abelian anyons
• Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions
• Topological blockade and measurement of topological charge
• Edge-Induced Qubit Polarization in Systems with Ising Anyons

Cited by in corpus (17)

• A Short Introduction to Topological Quantum Computation
• Superconducting analogue of the parafermion fractional quantum Hall states
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Braiding of Atomic Majorana Fermions in Wire Networks and Implementation of the Deutsch-Josza Algorithm
• Criticality in Translation-Invariant Parafermion Chains
• Braiding Majorana zero modes using quantum dots
• Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Effects of disorder on Coulomb-assisted braiding of Majorana zero modes
• Majorana fermions at the edge of superconducting islands
• Majorana fermion from Landau quantization in 2D topological superconductors
• Measurement-only topological quantum computation without forced measurements
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Topological Insulating Phases of Non-Abelian Anyonic Chains
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains