scholarly journals Nano-photoluminescence of natural anyon molecules and topological quantum computation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Alexander M. Mintairov ◽  
Dmitrii V. Lebedev ◽  
Alexei S. Vlasov ◽  
Alexei O. Orlov ◽  
Gregory L. Snider ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Fault Tolerant ◽  
Current Control ◽  
Molecular Structures ◽  
Quantum Field Theories ◽  
Many Body ◽  
Single Vortex ◽  
Charge Sensing ◽  
Topological Quantum ◽  
Topological Quantum Computation

AbstractThe proposal of fault-tolerant quantum computations, which promise to dramatically improve the operation of quantum computers and to accelerate the development of the compact hardware for them, is based on topological quantum field theories, which rely on the existence in Nature of physical systems described by a Lagrangian containing a non-Abelian (NA) topological term. These are solid-state systems having two-dimensional electrons, which are coupled to magnetic-flux-quanta vortexes, forming complex particles, known as anyons. Topological quantum computing (TQC) operations thus represent a physical realization of the mathematical operations involving NA representations of a braid group Bn, generated by a set of n localized anyons, which can be braided and fused using a “tweezer” and controlled by a detector. For most of the potential TQC material systems known so far, which are 2D-electron–gas semiconductor structure at high magnetic field and a variety of hybrid superconductor/topological-material heterostructures, the realization of anyon localization versus tweezing and detecting meets serious obstacles, chief among which are the necessity of using current control, i.e., mobile particles, of the TQC operations and high density electron puddles (containing thousands of electrons) to generate a single vortex. Here we demonstrate a novel system, in which these obstacles can be overcome, and in which vortexes are generated by a single electron. This is a ~ 150 nm size many electron InP/GaInP2 self-organized quantum dot, in which molecules, consisting of a few localized anyons, are naturally formed and exist at zero external magnetic field. We used high-spatial-resolution scanning magneto-photoluminescence spectroscopy measurements of a set of the dots having five and six electrons, together with many-body quantum mechanical calculations to demonstrate spontaneous formation of the anyon magneto-electron particles (eν) having fractional charge ν = n/k, where n = 1–4 and k = 3–15 are the number of electrons and vortexes, respectively, arranged in molecular structures having a built-in (internal) magnetic field of 6–12 T. Using direct imaging of the molecular configurations we observed fusion and braiding of eν-anyons under photo-excitation and revealed the possibility of using charge sensing for their control. Our investigations show that InP/GaInP2 anyon-molecule QDs, which have intrinsic transformations of localized eν-anyons compatible with TQC operations and capable of being probed by charge sensing, are very promising for the realization of TQC.

scholarly journals Competing ν = 5/2 fractional quantum Hall states in confined geometry

2016 ◽  
Vol 113 (44) ◽  
pp. 12386-12390 ◽  
Author(s):  
Hailong Fu ◽  
Pengjie Wang ◽  
Pujia Shan ◽  
Lin Xiong ◽  
Loren N. Pfeiffer ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Filling Factor ◽  
Fault Tolerant ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Quantum Point ◽  
Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

scholarly journals GEOMETRIC PHASES AND TOPOLOGICAL QUANTUM COMPUTATION

2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Geometric Phases ◽  
Quantum Phases ◽  
Topological Quantum ◽  
Universal Quantum ◽  
The Subject ◽  
Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.

scholarly journals SPIN NETWORK SETTING OF TOPOLOGICAL QUANTUM COMPUTATION

2005 ◽  
Vol 03 (01) ◽  
pp. 65-72 ◽  
Author(s):  
ANNALISA MARZUOLI ◽  
MARIO RASETTI
Keyword(s):  
Quantum Computation ◽  
Space Structure ◽  
Network Simulator ◽  
Quantum Field Theories ◽  
Fiber Space ◽  
Spin Network ◽  
Standard Quantum ◽  
Combinatorial Properties ◽  
Topological Quantum ◽  
Topological Quantum Computation

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the fiber space structure underlying the model which exhibits combinatorial properties closely related to SU (2) state sum models, widely employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.

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.

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

2021 ◽  
Vol 12 (1) ◽  
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

AbstractBraiding 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 coupling 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 the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization 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.

scholarly journals Systematic distillation of composite Fibonacci anyons using one mobile quasiparticle

2012 ◽  
Vol 12 (9&10) ◽  
pp. 876-892
Author(s):  
Ben W. Reichardt
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Success Probability ◽  
Quantum Algorithm ◽  
Systematic Construction ◽  
Topological Quantum ◽  
Universal Quantum ◽  
Measurement Devices ◽  
Topological Quantum Computation

A topological quantum computer should allow intrinsically fault-tolerant quantum computation, but there remains uncertainty about how such a computer can be implemented. It is known that topological quantum computation can be implemented with limited quasiparticle braiding capabilities, in fact using only a single mobile quasiparticle, if the system can be properly initialized by measurements. It is also known that measurements alone suffice without any braiding, provided that the measurement devices can be dynamically created and modified. We study a model in which both measurement and braiding capabilities are limited. Given the ability to pull nontrivial Fibonacci anyon pairs from the vacuum with a certain success probability, we show how to simulate universal quantum computation by braiding one quasiparticle and with only one measurement, to read out the result. The difficulty lies in initializing the system. We give a systematic construction of a family of braid sequences that initialize to arbitrary accuracy nontrivial composite anyons. Instead of using the Solovay-Kitaev theorem, the sequences are based on a quantum algorithm for convergent search.

scholarly journals In-plane magnetic field-driven symmetry breaking in topological insulator-based three-terminal junctions

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Jonas Kölzer ◽  
Kristof Moors ◽  
Abdur Rehman Jalil ◽  
Erik Zimmermann ◽  
Daniel Rosenbach ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Topological Insulator ◽  
Three Dimensional ◽  
Surface States ◽  
Output Terminal ◽  
Current Switch ◽  
Topological Quantum ◽  
Orbital Effect ◽  
Topological Surface ◽  
Topological Quantum Computation

AbstractTopological surface states of three-dimensional topological insulator nanoribbons and their distinct magnetoconductance properties are promising for topoelectronic applications and topological quantum computation. A crucial building block for nanoribbon-based circuits are three-terminal junctions. While the transport of topological surface states on a planar boundary is not directly affected by an in-plane magnetic field, the orbital effect cannot be neglected when the surface states are confined to the boundary of a nanoribbon geometry. Here, we report on the magnetotransport properties of such three-terminal junctions. We observe a dependence of the current on the in-plane magnetic field, with a distinct steering pattern of the surface state current towards a preferred output terminal for different magnetic field orientations. We demonstrate that this steering effect originates from the orbital effect, trapping the phase-coherent surface states in the different legs of the junction on opposite sides of the nanoribbon and breaking the left-right symmetry of the transmission across the junction. The reported magnetotransport properties demonstrate that an in-plane magnetic field is not only relevant but also very useful for the characterization and manipulation of transport in three-dimensional topological insulator nanoribbon-based junctions and circuits, acting as a topoelectric current switch.

Sign in / Sign up

Export Citation Format

Share Document