Braiding Majorana Fermions and Creating Quantum Logic Gates with Vortices on a Periodic Pinning Structure

Abstract

We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a CNOT gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.

14 pages, 25 figures

References in corpus (27)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Introduction to topological superconductivity and Majorana fermions
• Mechanics of Individual, Isolated Vortices in a Cuprate Superconductor
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Tunneling of anyonic Majorana excitations in topological superconductors
• Controlled Manipulation of Individual Vortices in a Superconductor
• Optical Manipulation of Single Flux Quanta
• Dipole-induced vortex ratchets in superconducting films with arrays of micromagnets
• Commensurability effects in superconducting Nb films with quasiperiodic pinning arrays
• Parity independence of the zero-bias conductance peak in a nanowire based topological superconductor-quantum dot hybrid device
• Nanoscale assembly of superconducting vortices with scanning tunnelling microscope tip
• Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state
• Fluxonic Cellular Automata
• Effect of hexagonal patterned arrays and defect geometry on the critical current of superconducting films
• Mott insulator phases and first-order melting in BSCCO crystals with periodic surface holes
• Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
• Pinning, Ordering, and Dynamics of Vortices in Conformal Crystal and Gradient Pinning Arrays
• Viscous Decoupling Transitions for Individually Dragged Particles in Systems with Quenched Disorder
• Hysteretic vortex matching effects in high-$T_c$ superconductors with nanoscale periodic pinning landscapes fabricated by He ion beam projection technique
• Vortex pinning by the point potential in topological superconductors: a scheme for braiding Majorana bound states
• Scheme for Majorana Manipulation Using Magnetic Force Microscopy
• Finite temperature effects on Majorana bound states in chiral $p$-wave superconductors
• Unzipping flux lines from extended defects in type-II superconductors

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• Control of Andreev bound states using superconducting phase texture
• Chiral Spin Textures for Next-Generation Memory and Unconventional Computing
• Braiding Majorana Zero Mode in An Electrically Controllable Way
• Unveiling non-Abelian statistics of vortex Majorana bound states in iron-based superconductors using fermionic modes
• Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems
• Supercurrent diode with high winding vortex
• Tunable Majorana corner states driven by superconducting phase bias in a vertical Josephson junction
• Active Rheology and Anti-Commensuration Effects For Driven Probe Particles on Two Dimensional Periodic Pinning Substrates
• Dynamical simulation of the injection of vortices into a Majorana edge mode
• Majorana bound states with chiral magnetic textures
• Scheme for braiding Majorana zero modes in vortices using an STT-matrix
• Scalable Gate-Defined Majorana Fermions in 2D p-Wave Superconductors