Protocol for reading out Majorana vortex qubit and testing non-Abelian statistics

Abstract

The successful test of non-Abelian statistics not only serves as a milestone in fundamental physics but also provides a quantum gate operation in topological quantum computation. An accurate and efficient readout scheme of a topological qubit is an essential step toward the experimental confirmation of non-Abelian statistics. In the current work, we propose a protocol to read out the quantum state of a Majorana vortex qubit on a topological superconductor island. The protocol consists of four Majorana zero modes trapped in spatially well-separated vortex cores on the two-dimensional surface of a Coulomb blockaded topological superconductor. Our proposed measurement is implemented by a pair of weakly coupled Majorana modes separately in touch with two normal metal leads, and the readout is realized by observing the conductance peak location in terms of gate voltage. Using this protocol, we can further test the non-Abelian statistics of Majorana zero modes in the two-dimensional platform. A successful readout of Majorana qubit is a crucial step towards the future application of topological quantum computation. In addition, this Coulomb blockaded setup can distinguish Majorana zero modes from Caroli-de Gennes-Matricon modes in vortex cores.

12 pages, 6 figures

References in corpus (62)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Search for Majorana fermions in superconductors
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Topological superconductors: a review
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Majorana Zero Modes and Topological Quantum Computation
• Exponential Protection of Zero Modes in Majorana Islands
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Majorana Fermion Induced Resonant Andreev Reflection
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Evidence for Majorana bound state in an iron-based superconductor
• Observation of topological superconductivity on the surface of an iron-based superconductor
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor
• Majorana mode in vortex core of Bi2Te3/NbSe2 topological insulator-superconductor heterostructure
• Quantized Majorana conductance
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor
• Majorana Fermions and Topology in Superconductors
• Measurement-Only Topological Quantum Computation
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Majorana box qubits
• Ballistic superconductivity in semiconductor nanowires
• Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe
• Observation of half-integer level shift of vortex bound states in an iron-based superconductor
• Low-lying Quasiparticle Excitations around a Vortex Core in Quantum Limit
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Helical Hinge Majoranas in Iron-Based Superconductors
• Spectroscopy of bulk and few-layer superconducting NbSe${}_2$ with van der Waals tunnel junctions
• Discrete energy levels of Caroli-de Gennes-Martricon states in quantum limit due to small Fermi energy in FeTe${}_{0.55}$Se${}_{0.45}$
• Tunneling of anyonic Majorana excitations in topological superconductors
• Conductance of a proximitized nanowire in the Coulomb blockade regime
• Controlled Manipulation of Individual Vortices in a Superconductor
• Thermodynamic phase diagram of Fe(Se${}_{0.5}$Te${}_{0.5}$) single crystals up to 28 Tesla
• Quantized conductance of Majorana zero mode in the vortex of the topological superconductor (Li0.84Fe0.16)OHFeSe
• Nonclassical correlations from randomly chosen local measurements
• London penetration depth and superfluid density in single crystals of Fe(Te,Se) and Fe(Te,S) superconductors
• Evolution of density of states and spin-resolved "checkerboard" pattern associated with Majorana bound state
• Conductance of a superconducting Coulomb blockaded Majorana nanowire
• A scanning tunneling microscope for spectroscopic imaging below 90 mK in magnetic fields up to 17.5 T
• Theory for Spin Selective Andreev Reflection in Vortex Core of Topological Superconductor: Majorana Zero Modes on Spherical Surface and Application to Spin Polarized Scanning Tunneling Microscope Probe
• Electronic structure of topological superconductors in the presence of a vortex lattice
• Tunneling into the vortex state of NbSe${}_2$ with van der Waals junctions
• Non-Abelian toplogical superconductors from topological semimetals and related systems under superconducting proximity effect
• Coulomb blockade of a nearly-open Majorana island

Cited by in corpus (7)

• Observation of half-integer level shift of vortex bound states in an iron-based superconductor
• Scalable Majorana vortex modes in iron-based superconductors
• Perspective: Challenges and Transformative Opportunities in Superconductor Vortex Physics
• Vortex Majorana braiding in a finite time
• Emergent vortex Majorana zero mode in iron-based superconductors
• A mesoscopic device for a realization of the Topological Kondo effect
• Scheme for braiding Majorana zero modes in vortices using an STT-matrix