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The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev... more
The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmion...
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We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors... more
We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors that form the topological and non-topological regions respectively. The hybridization of bound edge states results in spin currents and 4π-periodic torques, as a function of the relative magnetic field angle – an effect which is dual to the fractional Josephson effect. We establish relation between torques and spin-currents in the non-topological region where the magnetic field is almost zero and spin is conserved along the spin–orbit field direction. The angular momentum transfer could be detected by sensitive magnetic resonance force microscopy techniques
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The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance... more
The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks’ sparsity for both classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of quantum LDPC codes. Index Terms – Distance verification, complexity bounds, quantum stabilizer codes, LDPC codes, erasure correction
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Research Interests: Mathematics, Computer Science, Physics, Quantum Physics, Ising Model, and 5 morePhysical, Hypergraph, Cs/it, arXiv, and Logarithm
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Research Interests: Physics, Condensed Matter Physics, Solid State electronic devices, Electron, Physical sciences, and 12 moreImpurity, Dislocations, Two Dimensional Electron Gas, CHEMICAL SCIENCES, Anderson localization, Anomalous Hall effect, Berry phase, Scattering, Hall effect, Fermi Surface, spin-orbit interaction, and Point Defect
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Research Interests: Physics, Condensed Matter Physics, Giant Magnetoresistance, Quantum Mechanics, Nanomechanics, and 15 moreMagnetic field, Electrical Resistance, Electron Transport, Magnetization dynamics, Ferromagnetic Resonance, Magnetoresistance, Magnetization, Magnetic Anisotropy, Magnetic Resonance Force Microscopy, Ferromagnetism, Boundary Condition, Degree of Freedom, Angular Momentum, limit of detection, and diffusion equation
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We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both... more
We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette $\Z2$ gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of ``post-topological'' extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with finite rates the number of distinct classes of such extended defects is exponentially large, corresponding to extensive ground state entropy of these codes. Here, the transition can be driven by the entropy of the extended defects, a mechanism distinct from that in the local spin models where the number of defe...