Photonic implementation of majoranabased berry phases. As the environment is assumed to act locally in space, the kcm is a promising candidate for performing faulttolerant quantum computation. Topological quantum computing qc is a way of allowing precise quantum computations to run on noisy and imperfect hardware. Quantum holonomies for quantum computing international. Quantum computation and quantum information ebook by. In the hqc strategy information is encoded in degenerate eigenspaces of a parametric family of. We introduce anyons at the systemindependent level of anyon models and discuss. Use features like bookmarks, note taking and highlighting while reading introduction to. The berry phase is one of the most intriguing concepts in physics. Pachos zhenghanwang shors quantum factoring algorithm and the e.

A short introduction to topological quantum computation ville lahtinen, jiannis k. One of the most cited books in physics of all time, quantum computation and quantum information remains the best textboo. Kesselring 1, fernando pastawski 1, jens eisert 1, and benjamin j. The exotic statistics of anyons realized in physical systems can be interpreted as a topological version of geometric phases. The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize faulttolerant quantum.

In this book, a variety of different topics are presented together for the first time, forming a thorough introduction to topological quantum computation. Which parts of nielsen and chuangs textbook on quantum. Holonomic quantum computation hqc is an allgeometrical approach to quantum information processing. Introduction to topological quantum computation jiannis k. We explicitly show that the model is a hamiltonian realization of yetters homotopy 2type topological quantum field theory whereby the groundstate projector of the model defined on the manifold m3 is given by the partition function of the underlying topological quantum field theory for m3. Chapter 1 of mike and ike is still a good introduction to the history of quantum informa. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to. Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies alike. Cambridge core quantum physics, quantum information and quantum computation introduction to topological quantum computation by jiannis k.

Multiparticle aspects by demosthenes ellinas 1, giorgio kaniadakis 2, jiannis k. Introduction to topological quantum computation pachos. Pachos is a reader in the school of physics and astronomy at the university of leeds. Such a method of computing is a leading candidate for largescale qc. Pachos is a detailed resource on toric codes, speci. Recent citations introduction to topological quantum computation with nonabelian anyons bernard field and tapio simulafocus on topological quantum computation jiannis k pachos and steven h simonthis content was downloaded from ip address 157.

The study of topological quantum computation has extended far beyond the study of anyon braiding. Manipulations of these excitations enable the construction of a quantum computational model. As a single number one cannot expect it to capture all features of the ground state. He works on a variety of research topics, ranging from quantum. Quantum computation with abelian anyons on the honeycomb lattice by jiannis k. Introduction to topological quantum computation core.

This thesis deals with topological orders from two different perspectives. In the latter model, the topological invariance corresponds to the invariance of the geometric evolution against perturbations that are local in position space. Download now ideal for graduate students and researchers from various subdisciplines, this book provides an excellent introduction to topological quantum computation. Theoretical physics topological quantum computation topological insulators and superconductors. Pdf introduction to quantum information science download. Read quantum computation and quantum information 10th anniversary edition by michael a. The hardcover of the introduction to topological quantum computation by jiannis k.

Pachos 3 and antonio maria scarfone 4 1 qlab, school of electronic and computer engineering, technical university of crete, chania 73100, greece 2 department of applied science and technology, politecnico di torino, torino 10129, italy. This approach is inherently resilient against errors, thus promising to overcome one of the main obstacles for the realisation of quantum computers. Introduction to topological quantum computation by jiannis. We introduce anyons at the systemindependent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions. Brennena, demosthenes ellinasb, viv kendonc, jiannis k.

Furthermore, the possibility of realizing anyons in the rbm is discussed and an algorithm is given to build these anyonic excitations and braid them as a proof of concept for performing quantum gates and doing quantum computation. Quantum picturalism for topological clusterstate computing. 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. Topological aspects of quantum information processing.

A short introduction to topological quantum computation ville t. Pachos2, 1 freie universitat berlin, arnimallee 14, 14195 berlin, germany. This pedagogical introduction to topological quantum computation includes the following parts. Universal quantum computation with abelian anyon models. We introduce anyons at the systemindependent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. Pdf introduction to topological quantum computation.

Pdf a short introduction to topological quantum computation. Expressing an algorithm in terms of basic quantum gates makes it easy to evaluate its resources and complexity. Pdf restricted boltzmann machine representation for the. However, nonabelian statistics has not yet been demonstrated in the laboratory.

Mar 05, 2015 ill describe the things that i would add to nielsen and chuangs textbook hereafter referred to as mike and ike if i were a coauthor of its 2nd edition. This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers. Kesselring, fernando pastawski, jens eisert, and benjamin j. Pachos article in quantum information processing 116 december 2012 with 37 reads how we measure reads. A short introduction to topological quantum computation scipost. Pachos 1,3 school of physics and astronomy university of leeds leeds, uk abstract we consider topological quantum memories for a general class of abelian anyon models defined on. Entanglement measures for topological quantum states. A short introduction to topological quantum computation v.

Introduction to topological quantum computation by j. First we provide an introduction to anyons and topological models. University of cambridge damtp cambridge, uk october 2003 october 2006. In particular we consider the properties of anyons and their relation to topological quantum computation. Use features like bookmarks, note taking and highlighting while reading introduction to topological quantum computation.

Introduction to topological quantum computation by jiannis k. Introduction to topological quantum computation, jiannis k. Multiparticle aspects demosthenes ellinas 1, giorgio kaniadakis 2, jiannis k. A short introduction to topological quantum computation. Why should anyone care about computing with anyons. Keeping highlevel and technical language to a minimum, the author adopts a pedagogical style, making the book accessible to nonspecialists and researchers from a variety of subdisciplines. Available on amazon and at cambridge university press. Parafermions in a kagome lattice of qubits for topological quantum computation. Specific heat of 2d interacting majorana fermions from. The boundaries and twist defects of the color code. Universal quantum computation with abelian anyon models james r. We introduce anyons at the\ud systemindependent level of anyon models and discuss the key concepts of\ud protected fusion spaces and statistical quantum evolutions for encoding and\ud processing quantum information. Demosthenes ellinas, giorgio kaniadakis, jiannis k.

Introduction to topological quantum computation pachos, jiannis k. Pachos submitted on 11 may 2017 this version, latest version 12 sep 2017 v4 abstract. At the forefront of research in geometric evolutions is the controlled realization of anyonic statistics in condensed matter. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behaviour and establish their relation to quantum computation. The realization of majorana zero modes is in the centre of intense theoretical and experimental investigations. The boundaries and twist defects of the color code and their applications to topological quantum computation. Introduction to topological quantum computation 1, pachos. In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation.

By jiannis k pachos abstract ideal for graduate students and researchers from various subdisciplines, this book provides an excellent introduction to topological quantum computation. Third edition introduction to the theory of thermal neutron scattering g. Pachos school of physics and astronomy, university of leeds, leeds ls2 9jt, uk. Ill describe the things that i would add to nielsen and chuangs textbook hereafter referred to as mike and ike if i were a coauthor of its 2nd edition. Introduction to topological quantum computation university of leeds. Simulating the exchange of majorana zero modes with a. It inspired numerous investigations toward theoretical frontiers with its possible generalizations and technological applications in quantum computation. Introduction to topological quantum computation kindle edition by pachos, jiannis k download it once and read it on your kindle device, pc, phones or tablets.

Topological quantum computation is an approach to storing and manipulating quantum. They can encode information in a way that is protected from environmental perturbations. Topological systems can serve as quantum memories or as quantum computers. While the onequbit gates are performed dynamically the model offers the advantage of having a twoqubit gate that is of topological nature. We outline the general steps of topological quantum computation, as well as. Pachosc, ioannis tsohantjisb, zhenghan wangd acentre for quantum information science and security, macquarie university, 2109, nsw, australia bdepartment of sciences, division of mathematics, technical university of crete, gr 73 100, chania, crete, greece cschool of. One implementation uses surface codes created by forming defects in a highlyentangled cluster state. Entanglement measures for topological quantum states supervisor. We introduce anyons at the\ud systemindependent level of anyon models and discuss the key concepts of\ud protected.

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