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. 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. 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. They can encode information in a way that is protected from environmental perturbations. 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. Universal quantum computation with abelian anyon models. Use features like bookmarks, note taking and highlighting while reading introduction to topological quantum computation. We introduce anyons at the systemindependent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions. Entanglement measures for topological quantum states supervisor. 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. It inspired numerous investigations toward theoretical frontiers with its possible generalizations and technological applications in quantum computation. University of cambridge damtp cambridge, uk october 2003 october 2006. We consider a twodimensional spin system that exhibits abelian anyonic excitations. We introduce anyons at the systemindependent level of anyon models and discuss. However, nonabelian statistics has not yet been demonstrated in the laboratory. Introduction to topological quantum computation pachos, jiannis k. Theoretical physics topological quantum computation topological insulators and superconductors. 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.
Quantum computation and quantum information ebook by. A measurement of all the qubits at the end of the computation reveals the outcome. Brennena, demosthenes ellinasb, viv kendonc, jiannis k. 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. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to. Topological aspects of quantum information processing.
Kesselring, fernando pastawski, jens eisert, and benjamin j. Pachos zhenghanwang shors quantum factoring algorithm and the e. At the forefront of research in geometric evolutions is the controlled realization of anyonic statistics in condensed matter. Introduction to topological quantum computation by jiannis. The hardcover of the introduction to topological quantum computation by jiannis k. A common measure of quantum correlations is the entanglement entropy 1. Specific heat of 2d interacting majorana fermions from. Introduction to topological quantum computation jiannis k. While the onequbit gates are performed dynamically the model offers the advantage of having a twoqubit gate that is of topological nature. Overview of the current state of topological quantum computation and open questions. Introduction to topological quantum computation pachos.
Multiparticle aspects demosthenes ellinas 1, giorgio kaniadakis 2, jiannis k. Read quantum computation and quantum information 10th anniversary edition by michael a. Pdf introduction to quantum information science download. Download now ideal for graduate students and researchers from various subdisciplines, this book provides an excellent introduction to topological quantum computation. Introduction to topological quantum computation by j. He works on a variety of research topics, ranging from quantum. The realization of majorana zero modes is in the centre of intense theoretical and experimental investigations. Quantum holonomies for quantum computing international.
In particular we consider the properties of anyons and their relation to topological quantum computation. 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. Pachos school of physics and astronomy, university of leeds, leeds ls2 9jt, uk. As a single number one cannot expect it to capture all features of the ground state. A short introduction to topological quantum computation scipost. 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. By jiannis k pachos abstract ideal for graduate students and researchers from various subdisciplines, this book provides an excellent introduction to topological quantum computation. 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. 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. Introduction to topological quantum computation, jiannis k. Manipulations of these excitations enable the construction of a quantum computational model. The berry phase is one of the most intriguing concepts in physics.
Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies alike. Introduction to topological quantum computation core. Demosthenes ellinas, giorgio kaniadakis, jiannis k. Pachos is a reader in the school of physics and astronomy at the university of leeds. Cambridge core quantum physics, quantum information and quantum computation introduction to topological quantum computation by jiannis k. Such a method of computing is a leading candidate for largescale qc. Introduction to topological quantum computation university of leeds. This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers. In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. Third edition introduction to the theory of thermal neutron scattering g. In the latter model, the topological invariance corresponds to the invariance of the geometric evolution against perturbations that are local in position space. Introduction to topological quantum computation by jiannis k.
Use features like bookmarks, note taking and highlighting while reading introduction to. Chapter 1 of mike and ike is still a good introduction to the history of quantum informa. Pachos is a detailed resource on toric codes, speci. This thesis deals with topological orders from two different perspectives. Why should anyone care about computing with anyons. What are the best resources to learn topological phases from. The boundaries and twist defects of the color code. Pachos submitted on 11 may 2017 this version, latest version 12 sep 2017 v4 abstract. Parafermions in a kagome lattice of qubits for topological quantum computation. This pedagogical introduction to topological quantum computation includes the following parts. This approach is inherently resilient against errors, thus promising to overcome one of the main obstacles for the realisation of quantum computers. Ideal for graduate students and researchers from various subdisciplines, this book provides an excellent introduction to. First we provide an introduction to anyons and topological models. Pdf a short introduction to topological quantum computation.
Quantum computation with abelian anyons on the honeycomb lattice by jiannis k. The boundaries and twist defects of the color code and their applications to topological quantum computation. Topological systems can serve as quantum memories or as quantum computers. The study of topological quantum computation has extended far beyond the study of anyon braiding. A short introduction to topological quantum computation. Simulating the exchange of majorana zero modes with a. Available on amazon and at cambridge university press. Pdf restricted boltzmann machine representation for the. 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.
One of the most cited books in physics of all time, quantum computation and quantum information remains the best textboo. 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. University of leeds leeds, uk october 2006 present professor of theoretical physics. Topological quantum computing qc is a way of allowing precise quantum computations to run on noisy and imperfect hardware. Topological quantum computation is an approach to storing and manipulating quantum. A short introduction to topological quantum computation ville t. Introduction to topological quantum computation 1, pachos. 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. A short introduction to topological quantum computation v.
Which parts of nielsen and chuangs textbook on quantum. In the hqc strategy information is encoded in degenerate eigenspaces of a parametric family of. As the environment is assumed to act locally in space, the kcm is a promising candidate for performing faulttolerant quantum computation. A short introduction to topological quantum computation ville lahtinen, jiannis k. We introduce anyons at the\ud systemindependent level of anyon models and discuss the key concepts of\ud protected. 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. 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. Holonomic quantum computation hqc is an allgeometrical approach to quantum information processing. Pachos article in quantum information processing 116 december 2012 with 37 reads how we measure reads.
Pachos2, 1 freie universitat berlin, arnimallee 14, 14195 berlin, germany. Universal quantum computation with abelian anyon models james r. Ideal for graduate students and researchers from various subdisciplines, this book provides an excellent introduction to topological quantum computation topics. Multiparticle aspects by demosthenes ellinas 1, giorgio kaniadakis 2, jiannis k. We outline the general steps of topological quantum computation, as well as.
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