Topological quantum computationfrom basic concepts to. Download pdf classical and quantum computation book full free. A very rigorous book on the topic of quantum computation and complexity which builds up from classical complexity. The ams bookstore is open, but rapid changes related to the spread of covid19 may cause delays in delivery services for print products. These braids form the logic gates that make up the computer. Classical and quantum computation graduate studies in mathematics this book is an introduction to a new and rapidly developing topic. Literature to quantum computing of the international school for scientific computing 1 classical and quantum computing by yorick hardy and willihans steeb birkhauser publishing, basel, 2001 isbn 3764366109 2 hilbert spaces, wavelets, generalized functions and modern quantum mechanics by willihans steeb. This pedagogical introduction to topological quantum computation includes the following parts. This use of the kitaevfeynman clock for closed quantum systems was presented in 5. First we provide an introduction to anyons and topological models. Pdf classical and quantum computation download full pdf. Kitaev freedman kitaev, faulttolerant quantum computation by anyons 1997. Kitaev will lecture the second half of the first term, covering classical and quantum. Though nature seems to favor simplicity, she is also fond.
In these notes, we will learn that quantum computers di er from classical computation in several respects when it comes to the processing of the information. Landau institute for theoretical physics, kosygina st. One important problem is decoherence and systematic errors in unitary transformations which occur in real quantum systems. Blind topological measurementbased quantum computation. Faulttolerant quantum computation by anyons sciencedirect. Information can be identified as the most general thing which must propagate from a cause to an effect. It begins with the basics of classical theory of computation. Classical and quantum computation, volume 47 of graduate studies in mathematics. Topological quantum computation sits at the triple juncture of quantum topology, quantum physics, and quantum computation. A gentle introduction eleanor rieffel and wolfgang polak. 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. Nielsen and chuang, quantum computation and quantum information an encyclopedic reference for quantum information theory. Kitaev, fermionic quantum computation, annals of physics.
Kitaev will lecture the second half of the first term, covering classical and quantum algorithms and complexity. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. Quantum circuits are based on the quantum bit, or qubit, which is somewhat analogous to the bit in classical computation. Quantum computation and quantum information, nielsen and chuang cambridge university press, 2001 the bible of quantum computing. In this chapter, we shall give an account of the basic concepts and results in both classical and quantum computation theories, that will be used in the rest of the book. Another useful general reference is quantum computation and quantum information by nielsen and chuang nc. Qubits can be in a 1 or 0 quantum state, or they can be in a superposition of the 1 and 0 states. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing.
Mar 18, 2016 so computation is the main ingredient and component of both computational number theory and quantum computational number theory. For example, we cannot read a quantum data without having the state becoming. Classical physics turing model quantum mechanics quantum computing. Universal quantum computation with ideal clifford gates and noisy ancillas sergey bravyi and alexei kitaev institute for quantum information, california institute of technology, pasadena, 91125 california, usa sreceived 6 may 2004. A roadmap for a scalable topological quantum computer. Microsoft research, one microsoft way, redmond, wa 98052.
The world is quantum classical models of computation provide a level of abstraction discrete state systems devices are getting smaller moores law the only descriptions that work on the very small scale are quantum exploit quantum phenomena using quantum phenomena may allow us to perform. From the purely theoretical point of view, this problem has been solved due to shors discovery of faulttolerant quantum computation, with subsequent improvements. December, 20 one of the main problems with experimental realizations of quantum computation is performing the required operationsresiliently. Quantum computation there is a serious prospect for quantum physics to change the face of information science. Vyalyi, booktitlegraduate studies in mathematics, year2002. Classical structures in topological quantum computing. But alas, we are not so sure of our thesis at planck scale energies. We cover these topics at a very high level, just to give a sense of what you should know to understand the rest of the lecture notes. Pdf classical and quantum computation download full. Therefore, since the physical world is fundamentally quantum mechanical, the foundations of information theory and computer science should be sought in quantum physics. Then the authors introduce general principles of quantum computing and pass to the study of main quantum computation algorithms. Schematic of one of the scalable architectures for topological quantum computation proposed by karzig and colleagues.
Quantum computing and the entanglement frontier john preskill. If any of these topics are unfamiliar, you can learn more about them from a text on quantum computation. 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. Later, when the qof qprocessing is interpreted as genuine quantum feature, the. Topological quantum computation using majorana fermions. Topological quantum computation aims to achieve this goal by using nonabelian quantum phases of matter. Kitaev defined a quantum analogue of the classical class np and named it bqnp. This relation is rooted in the fact that the basic playground of qprocessing is the complex space hn generated by the set bnof binary vectors of length n, which is the basic arena of classical computation. Ph219cs219 quantum computation 200607 caltech particle. Physics 219 course information caltech particle theory. Quantum computing and the entanglement frontier john preskill visions of toc 29 may 20. Classical and quantum computation pdf free download.
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. Quantum information for the remainder of this lecture we will take a rst look at quantum information, a concept. The advantage of a quantum computer based on quantum braids. Mochon, anyons from nonsolvable groups are sufficient for universal quantum computation 2003.
Kitaev, shen and vyalyi, classical and quantum computation interesting but idiosyncratic. Classical and quantum computation american mathematical society. Volume ii deals with various important aspects, both theoretical and experimental, of quantum computation and information. Everyday low prices and free delivery on eligible orders. Linear operators for quantum mechanics thorough presentation of operators and mathematical structure.
Aim to use quantum mechanical phenomena that have no classical counterpart for computational purposes. It would also be useful to know something about classical information theory, classical coding theory, and classical complexity theory, since a central goal of the course will be generalize these topics to apply to quantum information. Kitaev is the author of classical and quantum computation 3. Unitary transformations can be performed by moving the excitations. Topological quantum computation zhenghan wang microsoft research station q, cnsi bldg rm 2237, university of. Topological quantum computation kitaev 97, flw 00 kitaev freedman. Search results for classicalandquantumcomputation classical and quantum computation.
Classical and quantum computation request pdf researchgate. Universal quantum computation with ideal clifford gates. Preskill and ogburn, topological quantum computation 1997. Classical and quantum computation graduate studies in. Quantum computational complexity, quantum information theory, quantum. Jan 01, 2002 a very rigorous book on the topic of quantum computation and complexity which builds up from classical complexity. Classical and quantum computation, kitaev, shen and vyalyi american mathematical society, 2002 a more concise introduction to many important topics in quantum computation.
Computers that perform quantum computation are known as a quantum computers i5 quantum computers are believed to be able to solve certain computational problems, such as integer factorization which underlies rsa encryption, significantly faster than. Memory states in a classical, or digital, computer can be written as a string of 0s and 1s. February 1, 2008 abstract a twodimensional quantum system with anyonic excitations can be considered as a quantum computer. Landau institute for theoretical physics, 117940, kosygina st. One was kitaevs idea of faulttolerant quantum computation by anyons ki1, and the other was freed. From reversible classical computations to quantum computations. The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. In classical computation, the unit of information is a bit, which can be 0 or 1. We study the topological quantum phase transition in the 2d kitaev honeycomb model by making use of the square root of the quantum jensenshannon divergence and find that the square root of the. In particular we consider the properties of anyons and their relation to topological quantum computation.
Vyalyi american mathematical society providence, rhode island graduate studies in mathematics. Classical and quantum computation available for download and read online in other formats. Furthermore, quantum gates are also increasingly vulnerable compared to their classical counterparts. Kitaev and others published classical and quantum computation find, read and cite all the research you need on. Blind quantum computation is a protocol that permits an algorithm, its input and output to be kept secret from the owner of the computational resource doing the calculation. Download classical and quantum computation graduate studies. I wouldnt recommend it as a first course but instead for a second course which focuses more on rigorous proofs. 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. Toffoli or controlnot needs little help to do universal quantum. Second, it is a useful tool for proving theorems about quantum computation, when the dynamics are no longer assumed to be unitary 8.
This book is an introduction to a new rapidly developing theory of quantum computing. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections. Classical and quantum computation semantic scholar. Classical and quantum computation graduate studies in mathematics book title. Universal quantum computation with ideal clifford gates and noisy ancillas sergey bravyi and alexei kitaev institute for quantum information, california institute of technology, pasadena, 91125 california, usa. Quantum computing is the use of quantummechanical phenomena such as superposition and entanglement to perform computation. Kitaev and others published classical and quantum computation find, read and cite all the research you need on researchgate. Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. So computation is the main ingredient and component of both computational number theory and quantum computational number theory. Turing machines, boolean circuits, parallel algorithms, probabilistic computation, npcomplete problems, and the idea of complexity of an algorithm.
John preskills quantum computation course at caltech. Topological quantum computation freedman 97, kitaev 97, fkw 00, flw 00. Topological quantum phase transitions in the 2d kitaev. Universal quantum computation with ideal clifford gates and. Are quantum computers more powerful than classical computers. Download classical and quantum computation graduate. Quantum computing lecture 1 university of cambridge. Classical and quantum computation, kitaev, shen and vyalyi. In this chapter, we shall give an account of the basic concepts and results in both classical and quantum computation. Classical and quantum computing university of johannesburg. Grovers algorithm, shors factoring algorithm, and the abelian hidden. The book starts with the basics of classical theory of computation, including npcomplete problems and the idea of complexity of an algorithm.
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