Topological quantum computation has emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. In physics, an anyon is a type of quasiparticle that occurs only in twodimensional systems, with properties much less restricted than fermions and bosons. Topological quantum computation is an approach to storing and manipulating quantum infor. Topological quantum computation, anyons and nonabelian. Furthermore, we show how topological quantum computation tqc can be performed with nonabelian anyons. Pdf developing a robust approach to implementing non. Topological quantum computers use particles with exotic exchange statistics called non abelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the fibonacci anyon model. Progress in theoretical chemistry and physics, vol 30. April 23, 2018 topological quantum computers promise a fault tolerant means to perform quantum computation.
Pdf nonabelian anyons and topological quantum computation. The mathematics describing the physics also can be quite. The current proposals for producing nonabelian anyons and majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. In particular we consider the properties of anyons and their relation to topological quantum computation. However, most systems do not have topological degrees of freedom. Topological quantum computation using nonabelian anyonsexotic particlelike excitations that are neither bosons nor fermionsas qubits. Quantum science and technology paper introduction to topological quantum computation with nonabelian anyons to cite this article. The advantage of a quantum computer based on quantum. Pdf error correction for nonabelian topological quantum.
Introduction to topological quantum computation with nonabelian. Despite the theoretical progress made during the past decade on using mzms in universal quantum computation 1417, due to the localized and pointlike nature of mzms, all existing proposed archi. Nonabelian statistics and topological quantum information. Nonabelian parton fractional quantum hall effect in. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized nonabelian geometric phases of degenerate ground states. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as it nonabelian anyons, meaning that they obey it nonabelian braiding. Topological quantum computation with nonabelian anyons in. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as \it non abelian anyons, meaning that they obey \it non abelian braiding. We show theoretically that the unique landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. The existence of topological phases of matter with nonabelian anyons would lead us to topological quantum computation via unitary modular tensor categories. Microscopically, topological orders correspond to patterns of longrange quantum. Topological quantum computing with majorana zero modes and. This idea was developed into topological quantum computation by kitaev in ann.
Error correction for nonabelian topological quantum computation. One way quantum computation 10 starts from a large entangled. Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. However, in an isingtype quantum hall state, the nonabelian anyons carry electrical charge, and one can imagine moving them by tuning electrical gates. Topological quantum computation from nonabelian anyons paul fendley experimental and theoretical successes have made us take a close look at quantum physics in two spatial dimensions. In physics, topological order is a kind of order in the zerotemperature phase of matter also known as quantum matter. The firm has been developing topological quantum computing for more than a decade and today has researchers writing software for future machines, and working with academic laboratories to craft. Introduction to topological quantum computation with nonabelian anyons bernard field and tapio simula school of physics and astronomy, monash university, victoria 3800, australia dated. Topological quantum computers use particles with exotic exchange statistics called nonabelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the fibonacci anyon. In this paper we present a theory of a nonabelian edgestate interferometer in a threedimensional topological insulator brought in proximity to an swave superconductor. Topological quantum computation based on chiral majorana. Nonabelian anyons and topological quantum computation.
Such phases allow for quantum information to be stored and manipulated in a nonlocal manner. Nonabelian anyons and topological quantum computation core. Majorana zero modes and topological quantum computation. One of them is the ability to perform any manipulation of your qubit. Tpm umtc tqc therefore the practical aspect of topological quantum computation hinges on the existence of nonabelian topological states. Introduction to topological quantum computation with non. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as \it nonabelian anyons, meaning that they obey \it non.
This pedagogical introduction to topological quantum computation includes the following parts. Topological quantum computation from nonabelian anyons. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but a re particles known as nonabelian anyons, meaning that they obey nonabelian braiding. Introduction to topological quantum computation with non abelian anyons bernard field and tapio simula school of physics and astronomy, monash university, victoria 3800, australia dated. Developing a robust approach to implementing nonabelian anyons and topological quantum computing in a modified kitaev honeycomb lattice model. Topological quantum computers promise a fault tolerant means to perform quantum computation. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy.
Interferometry of nonabelian edge excitations is a useful tool in topological quantum computing. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. These braids form the logic gates that make up the computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but a re particles known as non abelian anyons, meaning that they obey non abelian braiding statistics. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Pdf introduction to topological quantum computation. A short introduction to topological quantum computation. A topological quantum computer is a theoretical quantum computer that employs. This includes the fibonacci anyon model 9 and nonabelian quantum double models 6,7. Nonabelian anyons are exotic quasiparticles envisioned to be promising candidates for solidstate quantum computation. In this thesis we extend some of the results for abelian anyonic statistics to the case of nonabelian anyons. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as \it non abelian anyons, meaning that they obey \it non abelian. Related content braiding operators are universal quantum gates louis h kauffman and samuel j.
Nonabelian anyons, a species required for topological quantum computers, have. The computational answer is accessed by bringing anyons together and observing the. Exotic nonabelian anyons from conventional fractional. You need some criteria to perform computation at the quantum level. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as nonabelian anyons, meaning that they obey nonabelian. Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Nonabelian anyons statistical repulsion and topological quantum computation viktor qvarfordt masters thesis in mathematics supervised by douglas lundholm kth royal institute of technology and stockholm university 20170523 124. Topological quantum computation aims to achieve this goal by using nonabelian quantum phases of matter.
Anyons are generally classified as abelian or nonabelian. Simon4, ady stern5 1department of physics, university of maryland, college park, md 20742 2microsoft station q, university of california, santa barbara, ca 93108 3department of physics and astronomy, university of california. Majorana modes, nonabelian anyons, and topological. Information encoded in the degenerate state space of pairs of nonabelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing.
The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non abelian anyons, meaning that they obey non abelian braiding statistics. However the question of how to obtain and process information about what errors have. In this approach, information is stored in the lowest energy states of manyanyon systems and processed by braiding nonabelian anyons. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the.
Manipulating, braiding, and realizing nonabelian statistics of majorana fermions are all central to topological quantum computation although measurementonly approaches sidestep the braiding. There have been several proposals of quantum computation that are conceptually different, but equivalent to the circuit model. Topological quantum computation microsoft research. The statistical repulsion of nonabelian anyons is yet largely unexplored. This fact is particularly relevant from the perspective of quantum computation, since all known models that can achieve universality using topological operations alone have this kind of behavior. Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantum computationfrom basic concepts to. Error correction for nonabelian topological quantum. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as \it nonabelian anyons, meaning that. Topological quantum computation zhenghan wang ucsb math. The possibility of quantum computation using nonabelian anyons has been considered for over a decade.
I will brie y mention how quantum computation works in thisframework. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as \it nonabelian anyons, meaning. Non abelian anyons and topological quantum computation chetan nayak1,2, steven h. Topological phases of matter and non abelian anyons. Simon4, ady stern5 1department of physics, university of maryland, college park, md 20742 2microsoft station q, university of california, santa barbara, ca 93108 3department of physics and. Topological quantum computation using majorana fermions.
1421 1191 1542 345 739 564 930 768 575 513 981 632 551 427 338 63 997 462 1047 296 458 238 1535 763 276 880 593 1446 1065 279 187 40 895 1361 114 506 982 123 192