Jun 30, 2010 topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. A typeset version of chapter 8 on faulttolerant quantum computation is not yet available. 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. In the last twenty years, several themes have come to the forefront of quantum condensed matter physics research through crossfertilization with other disciplines, such as. May 29, 2010 topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. The k 3 readrezayi rr parafermion quantum hall state hosts nonabelian excitations which provide a platform for universal topological quantum computation. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum. Introduction to topological quantum computation 1, pachos. The work provides a good reference for quantum computation and quantum information courses, allowing for students to become familiar with major points on the quantum information theoretical aspects of topological quantum computation and the advantages of topological quantum computation for quantum noise resistance. Topological quantum computation microsoft research. Sets of topological superconductors containing six elements hexons, all hosting majorana zero modes mzms on the same side of the set, are interfaced with conventional superconductors and semiconductors to perform quantum computation. Sets of topological superconductors containing six elements hexons, all hosting majorana zero modes mzms on the same side of the set, are interfaced with conventional superconductors and semiconductors to perform. Introduction to topological quantum computation by jiannis.
Topological quantum computation regional conference series in. Hastings, chetan nayak,1,2 jason alicea,3,4 karsten flensberg, 5stephan plugge, 6 yuval oreg, 7 charles m. Chapter 2 kau man knot invariant and relation to physics 2. Inside microsofts quest for a topological quantum computer alex bocharov explains why the company is hoping to build qubits out of particles that some scientists think might not even exist. While quantum computers can achieve dramatic speedups over the classical computers familiar to us, identifying the origin of this quantum advantage in physical systems remains a major goal of quantum information science. In this approach, information is stored in the lowest energy states of manyanyon systems and processed by braiding nonabelian anyons. Topological quantum computation topological quantum computation tqc is a computational model built upon systems oftopological phases. Topological quantum computation encodes and manipulates information by exclusively employing anyons. For readers interested in the physics of topological. This will allow us to identify a hilbert space, where quantum information can be encoded faulttolerantly. Groups of particles similarly have quantum numbers topological quantum numbers. Topological quantum computation using majorana fermions.
Majorana zero modes and topological quantum computation npj. We sketch the background topology, discuss analogies such as topological entanglement and quantum entanglement, show direct correspondences. 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. We explore the mathematical foundations of topological quantum computation, a quantum computation model that is based on principles of topology which as a result is more resistant to quantum decoherence than existing models. In this approach, information is stored in the lowest energy states of manyanyon systems and processed by. Therefore, since the physical world is fundamentally quantum mechanical, the foundations of information theory and computer science should be sought in quantum physics.
We have made it easy for you to find a pdf ebooks without any digging. Therefore, for a system with many electrons, an operation that exchanges two of the electrons swaps their positions. The main sources for this paper were a paper by louis h. 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. Italian marriage in name only, jane austen in her own words, and many other ebooks. The book introduce a difficult concepts on topological quantum computing. May 31, 2017 topological qubits are among the more baffling, and if practical, more promising ways to approach scalable quantum computing. Scalable designs for quasiparticlepoisoningprotected topological quantum computation with majorana zero modes torsten karzig, 1christina knapp,2 roman m. Nonabelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a. A topological quantum computer is a theoretical quantum computer that employs twodimensional quasiparticles called anyons, whose world lines pass around. Scalable designs for quasiparticlepoisoningprotected.
The most advanced experimental e ort to build a topological quantum computer at this writing is fractional quantum hall quantum computation. The future of quantum computing could depend on this tricky qubit willett working in the clean metallization lab, where gallium arsenide crystals are coated with metal. Topological quantum computation caltech particle theory. Topological quantum computationfrom basic concepts to. Tqc qt qp qc the existence of topological phases of matter with nonabelian anyons would lead us to topological quantum computation via unitary modular tensor categories. Introduction to topological quantum computation ebook. The makings of topological systems, their properties and their computational power are presented in a pedagogical way. Pdf introduction to topological quantum computation. The number of physical qubits needed by the quantum hardware and the amount of time required to implement an algorithm is dictated by the manner in which this universal quantum state is consumed. A roadmap for a scalable topological quantum computer. Nonabelian anyons and topological quantum computation s.
Quantum information encoded in the charges of the quasiparticles is highly resistant to decoherence, and can be reliably processed by carrying one quasiparticle around another. Use features like bookmarks, note taking and highlighting while reading introduction to topological quantum computation. 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. A third framework is topological computation, in which qubits and operations are. Universal topological quantum computation from a superconductor. While this new paradigm holds incredible possibility, quantum computing is very much in its infancy. Clearly states what is needed to achieve such huge task. Topological quantum computation zhenghan wang ucsb math. Oct 27, 2015 topological quantum computation 1,2 is an approach to faulttolerant quantum computation in which the unitary quantum gates result from the braiding of certain topological quantum objects called. Information is something that can be encoded in the state of a physical system, and a computation is a task that can be performed with a physically realizable device. Quantum computation is the eld that investigates the computational power and other properties of computers based on quantummechanical principles. What are the prerequisites to study topological quantum. Kitaev, faulttolerant quantum computation by anyons.
Topological systems can serve as quantum memories or as quantum computers. Quantum computing since democritus by scott aaronson, quantum computation and quantum information by michael a. A twodimensional medium that supports abelian anyons has a topological. Topological qubits are among the more baffling, and if practical, more promising ways to approach scalable quantum computing. An important objective is to nd quantum algorithms that are signi cantly faster than any classical algorithm solving the same problem. This pedagogical introduction to topological quantum computation includes the following parts. If information is encoded in pairs of quasiparticles, then the aharonovbohm interactions can be adequate for universal faulttolerant quantum computation. 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 kitaev 97, flw 00 time. To fully embrace the power and potential of quantum computing, the system must be engineered to meet the demands of the solutions the. Although the rr state may be realized at the filling factor. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way.
A longwinded introduction on the history of this field the original string theorist 1867. Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Physics 219 course information caltech particle theory. 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. Inside microsofts quest for a topological quantum computer. Topological quantum systems university of copenhagen. To study the computational power of anyons we plan to look into their fusion and braiding properties in a systematic way. If you havent read the paper i would highly recommend it. A central theme of quantum theory is the concept of indistinguishable particles also called identical particles. The future of quantum computing could depend on this tricky. The idea to merge quantum mechanics and information theory arose in the 1970s but. In this book, a variety of different topics are presented together for the first time, forming a thorough introduction to topological quantum computation. A short introduction to topological quantum computation. Topological quantum computation ubc library open collections.
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 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 lecture note, we will focus on implementation of topological quantum computation with. That is, any of these models can efficiently simulate any of the others. Microsoft, purdue tackle topological quantum computer. This iceberg is a model of quantum computation based on topological, rather than local, degrees of freedom. In this paper we examine the problem of algorithmic optimisation in the topological lattice and introduce the required elements that will be needed. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner.
A gentle introduction eleanor rieffel and wolfgang polak. Pachos zhenghanwang shors quantum factoring algorithm and the e. First we provide an introduction to anyons and topological models. We say two knots are topologically equivalent if they can be deformed. Buy topological quantum computation regional conference series in. Quantum computation with topological codes from qubit to.
Topological quantum computation sits at the triple juncture of quantum topology, quantum physics, and quantum computation. For example, all electrons in the world are exactly alike. In particular we consider the properties of anyons and their relation to topological quantum computation. The book covers everything required to understand topological faulttolerant quantum computation, ranging from the definition of the surface code to topological. What is quantum computation and what makes it different from classical computation. Consequently, it is fruitful to move back and forth between quantum topological methods and the techniques of quantum information theory. Topological quantum computing is based on a model known as the toric code, which was introduced by alexei kitaev whom i learned the subject from back in 1997. Focus on topological quantum computation new journal of. I will then introduce the basic ideas behind topological quantum computation and demonstrate explicitly that certain nonabelian quasiparticles can indeed by used for universal quantum computation by showing how any quantum algorithm can be compiled into a braiding pattern for them. Topological quantum computation aims to achieve this goal by using nonabelian quantum phases of matter. 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. Topological quantum computation purdue engineering.
Were sorry but the topological materials database project doesnt work properly without javascript enabled. What is a zeroenergy majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation. Schematic of one of the scalable architectures for topological quantum computation proposed by karzig and colleagues. Oct 21, 2016 inside microsofts quest for a topological quantum computer alex bocharov explains why the company is hoping to build qubits out of particles that some scientists think might not even exist. The computational answer is accessed by bringing anyons together and observing the result. Topological quantum computers are equivalent in computational power to other standard models of quantum computation, in particular to the quantum circuit model and to the quantum turing machine model. This book expands on the authors cbms lectures on knots and topological quantum. A topological quantum field theory is a quantum field theory which as a functorial quantum field theory is a functor on a flavor of the.
I am an undergraduate student and i would like to approach the subject of topological order with focus on topological quantum computation, i know very little qft and basic algebraic topology if. Then, we describe how abelian anyons can be found in a. A useful tool here is measurementbased quantum computation mqc, a computational framework utilizing the quantum entanglement. From the generalization of the topological basis for the two. The computational answer is accessed by bringing anyons together and observing the.
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. Islamic family law in a changing world a global resource book, it essentials chapter 3 test, and many other ebooks. As quantum technologies advance, we get closer to finding solutions to some of the worlds most challenging problems. Topological quantum computation 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.
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