Professor kang wang ucla presents his invited lecture on chiral majorana and topological quantum computing at the kavli futures symposium on the frontiers of condensed matter physics, hosted. 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. Library of congress cataloginginpublication data rieffel, eleanor, 1965 quantum computing. Topological quantum computation using majorana fermions. The aim of these lectures is to explain these important results. Topological quantum computation zhenghan wang ebok. Quantum anomalous hall effectthe appearance of quantized hall conductance at zero magnetic fieldhas been observed in thin films of the topological insulator bi2se3 doped with magnetic atoms. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories.
First we provide an introduction to anyons and topological models. Harvard researchers have demonstrated the first material that can have both strongly correlated electron interactions and topological properties. Nonabelian anyons and topological quantum computation s. Cbms regional conference series in mathematics publication year 2010. In a quantum computer, errors are continuous, not just bit ips. The quantum spy author david ignatius on the future of high. This pedagogical introduction to topological quantum computation includes the following parts. Researchers find a platform for stable quantum computing. Oct 21, 2016 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.
With an emphasis on introducing basic notions and current research, this book gives the first coherent account. Two groups have now observed quantum anomalous hall effect in. This recent paper of 2016 contains a useful introduction to the new development in tqft for strongly coupled condensed matter system and topological quantum matter in 3dimensions, 4dimensions and any dimension. Possessing a good knowledge of linear algebra, something that would be covered in a undergraduate course perhaps, is fairly important to ensure you get as much as you can out of reading this text. Then, we define quantum bits and gates to set the stage for quantum computing. This book was set in syntax and times roman by westchester book group. Introduction to topological quantum computation university of leeds. A new model in topological quantum computing, named gravitational.
Jun 30, 2010 topological quantum computation by zhenghan wang, 9780821849309, available at book depository with free delivery worldwide. Part of the lecture notes in computer science book series lncs, volume 4618. Microsoft, purdue tackle topological quantum computer. Universal quantum computation with metaplectic anyons. Professor steve simon, department of physics at oxford university, lectures on topological quantum computing. The quantum spy author david ignatius on the future of. Recent years have seen an explosion in research efforts discovering and understanding novel electronic and optical properties of topological quantum materials tqms. Nov 27, 2017 the intersection of quantum computing and espionage may feel like a faraway future. The advantage of a quantum computer based on quantum. The braiding and fusion of anyonic excitations in quantum hall electron liquids and 2dmagnets are modeled by modular functors. We start with waveparticle duality and quantum puzzles to get the reader familiar with intriguing quantum ideas.
In this ldrd, a synergistic effort of materials growth, characterization, electricalmagnetooptical measurements, combined with. 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 quantum computation zhenghan wang ucsb math. Topological insulators that can sustain a persistent spinlocked current on their surfaces which does not decay are termed symmetry protected, and that state is compelling for multiple revolutionary device concepts in quantum computing and spintronics, said jigang wang, ames laboratory physicist and iowa state university professor. The braiding and fusion of anyonic excitations in quantum hall electron liquids and 2dmagnets are modeled by modular functors, opening a new. Study discovers lightinduced switching mechanism in dirac. Zhenghan wang topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. Topological quantum computing topological phases of matter are quantum computers, and form the foundation for building a scalable universal quantum computer. A complete electronic band theory is presented that describes the global properties of all possible band structures and materials, and can be used to predict new topological insulators and semimetals. Topological quantum computation is an approach to storing and. In this approach, information is stored in the lowest energy states of manyanyon systems and processed by braiding nonabelian anyons. Introduction to topological quantum computation by jiannis k. Finally, we touch upon quantum algorithms and quantum machine learning very briefly. At least thats what microsoft, purdue university, and three other universities are hoping after having recently signed a fiveyear agreement to develop a topological qubit based quantum computer.
But in his latest novel, david ignatius, washingtons own john le carre, tackles just that. Topological insulators have nontrivial symmetryprotected topological order. Topological quantum computation by zhenghan wang, 9780821849309. Abramsky, coecke, and others studied quantum information extensively from a categorical point of view, and found many applications in tensor networks 12.
So we mainly cite original references, expository surveys, and books. May 29, 2010 topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. Scientists who study topological materials face a challengehow to establish and maintain control of these unique quantum behaviors in a way that makes applications like quantum computing possible. In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. The book tells the story of 2d spintronics in a systematic and comprehensive way, providing the growing community of spintronics researchers with a key reference. The search for a largescale, errorfree quantum computer is reaching an intellectual junction at which semiconductor physics, knot theory, string theory, anyons, and quantum hall effects are all coming together to produce quantum immunity. In this chapter we describe a combinatorial framework for topological quantum computation, and illustrate a number of algorithmic questions in knot theory and in the theory of finitely presented groups, focusing in particular on the braid group. For readers interested in the physics of topological quantum. The braiding and fusion of anyonic excitations in quantum hall electron. The hopf algebra axioms were studied in tensor networks by lafont.
Christian schmid, ady stern, david tong, zhenghan wang, harald weinfurter. The doping, however, introduces inhomogeneity, reducing the temperature at which the effect occurs. A topological quantum computer is a theoretical quantum computer that employs twodimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a threedimensional spacetime i. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field. Ising anyons 17 4 quantum computation with anyons 19 4. A reading list for topological quantum field theory. Introduction to topological quantum computing steven h. Topological qubits are among the more baffling, and if practical, more promising ways to approach scalable quantum computing.
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. These braids form the logic gates that make up the computer. Our topological classical computing theorems are analogs of the famous results of freedman, larsen and wang establishing the quantum universality of topological quantum computing with the jones. In the case of topological quantum computing, a qubit is encoded in non local properties of a system and hence is not subject to change under any local perturbations on the system. With an emphasis on introduction to basic notions and current research, the book is almost entirely about the mathematics of topological quantum computation. Since measurement destroys the superposition, how do we know errors have occurred. 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.
In particular we consider the properties of anyons and their relation to topological quantum computation. This book expands on the authors cbms lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. This clear, practical book takes quantum computing out of the realm of theoretical physics and teaches the fundamentals of the field to students and professionals who have not had training in quantum computing or quantum information theory, including computer scientists, programmers, electrical engineers, mathematicians, physics students, and chemists. This book expands the plan of the authors 2008 nsfcbms lectures on knots and topological quantum computing, and is intended as a primer for. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. Part one addresses the fundamental theoretical aspects of 2d materials and spin transport, while parts two through four explore 2d material systems, including graphene, topological. It is here that the proposals for topological quantum computing seem promising4,10,11. Topological quantum computation american mathematical society. Proceedings of the nsfcbms regional conference in the mathematical sciences on topological quantum computing held at the university. Kang wang on chiral majorana and topological quantum. Topological quantum computation microsoft research. A longwinded introduction on the history of this field the original string theorist 1867.
Topological quantum materials for quantum computation. Inside microsofts quest for a topological quantum computer. Topological quantum systems university of copenhagen. The authors point out the relations between quantum hamiltonian lattice models, the continuum tqfts and group cohomologycobordism. Simulation of topological field theories by quantum computers, commun. We demonstrate the dynamic stabilization in topological matter as a new universal tuning knob, that can be used to reinforce protected quantum transport, said wang.
May 31, 2017 topological qubits are among the more baffling, and if practical, more promising ways to approach scalable quantum computing. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. In this book, a variety of different topics are presented together for the first time, forming a thorough introduction to topological quantum computation. Abstract for topological quantum computing for beginners, by john preskill i will describe the principles of faulttolerant quantum computing, and explain why topological approaches to fault. The intersection of quantum computing and espionage may feel like a faraway future. A topological phase is a class of gapped hamiltonians that realize the same tqft or anyon model in low energy. Topological quantum computing topological phases of matter are quantum computers, and form the. However, enormous scientific and engineering challenges must be overcome for scalable quantum computers to be realized. This gives rises to the topological quantum information braiding particles with nonabelian statistics entangled and i shall talk more about it in the end of this work. A twodimensional quantum system with anyonic excitations. Quantum computers should be capable of performing tasks that would be very difficult, if not impossible, with digital computers, such as finding the prime factors of large numbers, searching large databases, and simulating quantum systems. In mathematical terms, these are unitary topological modular functors.
Simulation of topological field theoriesby quantum computers. A gentle introduction eleanor rieffel and wolfgang polak. The implications are farreaching, from the predicted existence of quasiparticles with nonabelian exchange statistics to novel approaches to quantum computing where the topology of qubit protects it against decoherence. They underlie the jones polynomial and arise in wittenchernsimons theory. The theory of quantum computation can be constructed from the abstract study of anyonic systems. The main topic was connections between quantum information and black holes. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. A twodimensional medium that supports abelian anyons has a topological. Topological quantum computation is a paradigm to build a large scale quantum computer based on topological phases of matter. The computational answer is accessed by bringing anyons together and observing the. Gravitational topological quantum computation springerlink. Introduction to topological quantum computation by jiannis.
Wang and kitaev showed in 2002,fklw02, that a topological quantum computer can simulate any computation of a standard quantum computer. We will focus on the applications of anyons to quantum computing, not. In this experiment, jigang wang and his colleagues demonstrated that control by using light to steer quantum states in a dirac semimetal. Here we provide a very simple explanation of what quantum computing is, the key promises of quantum computers and how. Topological quantum computation mathematical association of. The lecture is the first of two parts, and was filmed at the canadian summer school on. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to. The topological ground states of the system are therefore sep.
Abstract for topological quantum computing for beginners, by john preskill i will describe the principles of faulttolerant quantum computing, and explain why topological approaches to fault tolerance seem especially promising. In this survey, we discuss the conceptual development of this. In topological quantum computing, information is encoded in knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. This book is a sort of travel guide through topological quantum computation it is composed of four parts, preliminaries that introduce quantum mechanics, part two that deals with topological phases of matter and part three that deals with theories of topological quantum matter. In topological quantum computing, information is encoded in knotted quantum. A topological insulator is a material that behaves as an insulator in its interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material. This book expands on the authors cbms lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate. Freedman, kitaev, and wang, simulation of topological field theories by quantum computers 2000.
Quantum anomalous hall effect in intrinsic magnetic. For the second half of the term, the main topic is topological quantum computing jp chapter 9. Even considering that the simulation is approximate, given any accuracy, a braid can be found, and it will simulate the computation to that accuracy. The discovery both paves the way for more stable quantum computing and creates an entirely new platform to. Pdf topological quantum computing with only one mobile. Wang, topological quantum computation amer mathematical society, 2010, vol. When i first was getting into quantum computing, this book served as a rosetta stone for many of the concepts that were at first foreign to me. The computational answer is accessed by bringing anyons together and observing the result. In the tech and business world there is a lot of hype about quantum computing. A short introduction to topological quantum computation. Combinatorial framework for topological quantum computing. Larsen, and wang 63 proved that for certain types of nonabelian. Quantum computing since democritus by scott aaronson, quantum computation and quantum information by michael a.
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