Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State

Abstract

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at Landau level filling fraction $\nu =5/2$. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the $\nu =5/2$ state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically-protected qubit on which a logical NOT operation is performed by quasiparticle braiding. Using the measured excitation gap at $\nu =5/2$, we estimate the error rate to be $10^{-30}$ or lower.

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• Incompressible Liquid, Stripes and Bubbles in rapidly rotating Bose atoms at $\nu =1$
• Alternation and interchange of e/4 and e/2 period interference oscillations as evidence for filling factor 5/2 non-Abelian quasiparticles
• Simulation of non-Abelian Anyons using ribbon operators connected to a common base site
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Edge-Induced Qubit Polarization in Systems with Ising Anyons
• Tunnelling current through fractional quantum Hall interferometers
• Entanglement Generation by Communication using Phase-Squeezed Light with Photon Loss
• Identification of the Fractional quantum Hall edge modes by density oscillations
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Topological Single Electron Pumping Assisted by Majorana Fermions
• In-plane electric fields and the $\nu =\frac{5}{2}$ fractional quantum Hall effect in a disk geometry
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Neutral excitation and bulk gap of the Fractional Quantum Hall liquids in disk geometry
• Probing Kitaev Models on Small Lattices
• Aharonov-Bohm effect and coherence length of charge e/4 quasiparticles at 5/2 filling factor measured in multiple small Fabry-Perot interferometers
• Realizing Universal Majorana Fermionic Quantum Computation
• Increasing complexity with quantum physics
• Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Floquet-engineered diode performance in a Majorana-quantum dot Josephson junction
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States
• Topological phase transition driven by magnetic field in one-dimensional topological superconductor rings
• Stability of the 5/2 Fractional Quantum Hall State in a Corbino Disc Sample with In-plane Electric Fields
• Decoherence of high-energy electrons in weakly disordered quantum Hall edge states
• Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks
• General scheme for preparation of different topological states on the cluster states
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Correlated transport of FQHE quasiparticles in a double-antidot system
• Interlayer Diffusion of Nuclear Spin Polarization in $\nu =2/3$ Quantum Hall States
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Formation of spin droplet at nu = 5/2 in an asymmetric quantum dot under quantum Hall conditions
• Evolution of the Chern Gap in Chern Magnet HoMn${}_6$Sn${}_{6-x}$Ge${}_x$
• Topologically protected qubits as minimal Josephson junction arrays with non trivial boundary conditions: a proposal
• Taking stock of the quantum Hall effects: Thirty years on
• Emulating Non-Abelian Topological Matter in Cold Atom Optical Lattices
• Quantum Hall interferometry at finite bias with multiple edge channels
• A non-invasive method for nanoscale electrostatic gating of pristine materials
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• From Majorana fermions to topological quantum computation in semiconductor/superconductor heterostructures
• Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Majorana Fermions Under Uniaxial Stress in Semiconductor-Superconductor Heterostructures
• Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
• Engineering Majorana corner modes from two-dimensional hexagonal crystals
• Majorana Fermions in Semiconducting Nanowires on the Top of Fulde-Ferrell Superconductor
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Universal quantum control over Majorana zero modes
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Majorana modes in helical altermagnet without net magnetism and spin-orbit coupling
• Supersymmetric Hamiltonian Approach to Edge Excitations in $\nu =5/2$ Fractional Quantum Hall Effect
• Computational equivalence of the two inequivalent spinor representations of the braid group in the Ising topological quantum computer
• Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
• Knots and signal transmission in topological quantum devices
• Entangling spin and charge degrees of freedom in semiconductor quantum dots
• How should we choose the boundary conditions in a simulation which could detect anyons in one and two dimensions?
• Braiding properties of paired spin-singlet and non-abelian hierarchy states
• Interferometry versus projective measurement of anyons
• Chiral Spin Textures of Strongly Interacting Particles in Quantum Dots
• Dynamics of edge Majorana fermions in $\nu =\frac{5}{2}$ fractional quantum Hall effects
• Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
• Spin-flux attachment by dimensional reduction of vortices
• Edge mode velocities in the quantum Hall effect from a dc measurement
• Twisted Interferometry: the topological perspective
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model
• Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Landau levels for discrete-time quantum walks in artificial magnetic fields
• Robust Majorana bound state in pseudo-spin domain wall of 2-D topological insulator
• Measuring the Spin Polarization of a Ferromagnet: an Application of Time-Reversal Invariant Topological Superconductor
• Twisted Interferometry
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• Time-domain anyon interferometry in Kitaev honeycomb spin liquids and beyond
• Exact modular $S$ matrix for the ${\mathbb{Z}}_k$ parafermion quantum Hall islands and measurement of non-Abelian anyons
• Manipulating Edge Majorana Fermions in Vortex State
• Topological Quantum Computation with the universal R matrix for Ising anyons
• Triple Antidot Molecules
• Examples of Enhanced Quantization: Bosons, Fermions, and Anyons
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Conformal field theory description of mesoscopic phenomena in the fractional quantum Hall effect
• SWAP gate between a Majorana qubit and a parity-protected superconducting qubit
• Extracting the scaling dimension of quantum Hall quasiparticles from current correlations
• Scanning tunneling microscopy study of helimagnetic monolayer CrBr2 on s-wave superconductor NbSe2: a topologically trivial system due to weak interfacial coupling
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor