scholarly journals Zero modes, bosonization, and topological quantum order: The Laughlin state in second quantization

2015 ◽  
Vol 91 (8) ◽  
Author(s):  
Tahereh Mazaheri ◽  
Gerardo Ortiz ◽  
Zohar Nussinov ◽  
Alexander Seidel
Keyword(s):  
Second Quantization ◽  
Zero Modes ◽  
Topological Quantum ◽  
Quantum Order

scholarly journals Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lingyuan Kong ◽  
Lu Cao ◽  
Shiyu Zhu ◽  
Michał Papaj ◽  
Guangyang Dai ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Zero Mode ◽  
Scanning Tunneling ◽  
Homogeneous Material ◽  
Dirac Fermions ◽  
Tunneling Microscopy ◽  
Zero Modes ◽  
Topological Quantum ◽  
One Step ◽  
Topological Quantum Computation

AbstractThe iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

scholarly journals Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes

2017 ◽  
Vol 95 (23) ◽  
Author(s):  
Torsten Karzig ◽  
Christina Knapp ◽  
Roman M. Lutchyn ◽  
Parsa Bonderson ◽  
Matthew B. Hastings ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Zero Modes ◽  
Topological Quantum ◽  
Topological Quantum Computation

scholarly journals Search for non-Abelian Majorana braiding statistics in superconductors

2020 ◽  
Author(s):  
Carlo Beenakker
Keyword(s):  
Quantum Information ◽  
Parameter Space ◽  
Quantum Information Processing ◽  
Fusion Rule ◽  
Real Space ◽  
Edge Mode ◽  
Zero Modes ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Basic Concepts

This is a tutorial review of methods to braid non-Abelian anyons (Majorana zero-modes) in topological superconductors. That ``Holy Grail'' of topological quantum information processing has not yet been reached in the laboratory, but there now exists a variety of platforms in which one can search for the Majorana braiding statistics. After an introduction to the basic concepts of braiding we discuss how one might be able to braid immobile Majorana zero-modes, bound to the end points of a nanowire, by performing the exchange in parameter space, rather than in real space. We explain how Coulomb interaction can be used to both control and read out the braiding operation, even though Majorana zero-modes are charge neutral. We ask whether the fusion rule might provide for an easier pathway towards the demonstration of non-Abelian statistics. In the final part we discuss an approach to braiding in real space, rather than parameter space, using vortices injected into a chiral Majorana edge mode as ``flying qubits''.

scholarly journals A Short Introduction to Topological Quantum Computation

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Ville Lahtinen ◽  
Jiannis Pachos
Keyword(s):  
Quantum Computation ◽  
Condensed Matter ◽  
Quantum Computers ◽  
Short Introduction ◽  
Entry Level ◽  
Zero Modes ◽  
Topological Quantum ◽  
Topological Quantum Computation ◽  
Superconducting Nanowire ◽  
Energy Physics

This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons. We introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. Both the encoding and the processing are inherently resilient against errors due to their topological nature, thus promising to overcome one of the main obstacles for the realisation of quantum computers. We outline the general steps of topological quantum computation, as well as discuss various challenges faced by it. We also review the literature on condensed matter systems where anyons can emerge. Finally, the appearance of anyons and employing them for quantum computation is demonstrated in the context of a simple microscopic model -- the topological superconducting nanowire -- that describes the low-energy physics of several experimentally relevant settings. This model supports localised Majorana zero modes that are the simplest and the experimentally most tractable types of anyons that are needed to perform topological quantum computation.

scholarly journals A new Majorana platform in an Fe-As bilayer superconductor

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Wenyao Liu ◽  
Lu Cao ◽  
Shiyu Zhu ◽  
Lingyuan Kong ◽  
Guangwei Wang ◽  
...  
Keyword(s):  
Bound States ◽  
Zero Mode ◽  
Surface States ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Iron Pnictide ◽  
Iron Chalcogenide ◽  
Zero Modes ◽  
Topological Quantum ◽  
Iron Chalcogenide Superconductors

Abstract Iron-chalcogenide superconductors have emerged as a promising Majorana platform for topological quantum computation. By combining topological band and superconductivity in a single material, they provide significant advantage to realize isolated Majorana zero modes. However, iron-chalcogenide superconductors, especially Fe(Te,Se), suffer from strong inhomogeneity which may hamper their practical application. In addition, some iron-pnictide superconductors have been demonstrated to have topological surface states, yet no Majorana zero mode has been observed inside their vortices, raising a question of universality about this new Majorana platform. In this work, through angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy measurement, we identify Dirac surface states and Majorana zero modes, respectively, for the first time in an iron-pnictide superconductor, CaKFe4As4. More strikingly, the multiple vortex bound states with integer-quantization sequences can be accurately reproduced by our model calculation, firmly establishing Majorana nature of the zero mode.

scholarly journals Topological quantum order: Stability under local perturbations

2010 ◽  
Vol 51 (9) ◽  
pp. 093512 ◽  
Author(s):  
Sergey Bravyi ◽  
Matthew B. Hastings ◽  
Spyridon Michalakis
Keyword(s):  
Local Perturbations ◽  
Topological Quantum ◽  
Quantum Order

scholarly journals Integrating micromagnets and hybrid nanowires for topological quantum computing

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Malcolm Jardine ◽  
John Stenger ◽  
Yifan Jiang ◽  
Eline J. de Jong ◽  
Wenbo Wang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Quantum Computing ◽  
External Magnetic Field ◽  
Numerical Simulations ◽  
Hybrid Systems ◽  
Scaling Up ◽  
Magnet Design ◽  
Zero Modes ◽  
Magnetic Imaging ◽  
Topological Quantum

Majorana zero modes are expected to arise in semiconductor-superconductor hybrid systems, with potential topological quantum computing applications. One limitation of this approach is the need for a relatively high external magnetic field that should also change direction at the nanoscale. This proposal considers devices that incorporate micromagnets to address this challenge. We perform numerical simulations of stray magnetic fields from different micromagnet configurations, which are then used to solve for Majorana wavefunctions. Several devices are proposed, starting with the basic four-magnet design to align magnetic field with the nanowire and scaling up to nanowire T-junctions. The feasibility of the approach is assessed by performing magnetic imaging of prototype patterns.

scholarly journals Observation of magnetic adatom-induced Majorana vortex and its fusion with field-induced Majorana vortex in an iron-based superconductor

2020 ◽  
Author(s):  
Peng Fan ◽  
Fazhi Yang ◽  
Guojian Qian ◽  
Hui Chen ◽  
Yu-Yang Zhang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Bound States ◽  
Zero Mode ◽  
Fault Tolerant ◽  
Abrikosov Vortex ◽  
Zero Modes ◽  
Topological Quantum ◽  
Iron Based ◽  
Dual Origin ◽  
Single Material

Abstract Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the fusion of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and Majorana zero mode induced by magnetic Fe adatoms deposited on the surface and the realization of its fusion with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

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