In sections 2, 3 and 4 of this tutorial, we describe the mathematics needed for quantum computation together with an overview of the theory of quantum computation. Quantum information theory and the foundations of quantum. Quantum computation and quantum information michael pdf. Introduction to quantum information university of glasgow. The mathematics of quantum mechanics university of. The state of a quan turn computer is described by a wavefunction or a state in a hilbert space, and quantum information theory con siders the transmission of quantum states from source to receiver.
Request pdf on jan 1, 2011, masanori ohya and others published mathematical foundations of quantum information and computation and its applications to nano and biosystems find, read and cite. This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. Just as classical physics uses calculus to explain nature, quantum physics uses quantum mechanics to explain nature. Mathematical foundations of quantum information and computation and its. In some cases quantum algorithms can be used to perform computations faster than in any known classical algorithm. Quantum computation and quantum information by michael nielsen and isaac chuang, will prokofiev sheet music pdf be available in the fall of 2000.
Chuang cambridge, 2000 in addition the book consistent quantum theory by r. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of. Mathematical foundations of quantum information and computation. Mathematical formulation of quantum mechanics wikipedia. Quantum computation is the eld that investigates the computational power and other properties of computers based on quantummechanical principles. Griffiths cambridge 2002 is recommended for part i of the course. Mathematical foundations of topological quantum computation 3 thus this tells us that the symmetric group action, as showed brie y before, isnt the only group at work here since the path that the particle takes a ects the phase factor acquired under exchange.
In physics and computer science, quantum information is the information of the state of a quantum system. Centre for quantum information and foundations centre. Just as classical computers can be thought of in boolean algebra terms, quantum computers are reasoned about with quantum mechanics. One of the goals of quantum computation and quantum information is to develop tools which sharpen our intuition about quantum mechanics, and make its. Mathematical foundations of quantum information john watrous department of computer science university of calgary. Shannons noiseless coding theorem, using much the same mathematical ideas. Pdf mathematical foundations of information theory. Since the publication of the preceding book quantum information.
Mathematical foundations of quantum mechanics wikipedia. Quantum computation and quantum information by michael. Topological quantum computation 10 acknowledgements 11 revisions 11 references 11 1. Taken together, these two improvements allow a better analysis of quantum state transmission. Theory of quantum data and data processing quantum data. Overview so far, we have been using a simple mathematical framework for discussing quantum information. The josephson junction is the basic building block of a superconducting qubit, and thus a quantum computer. In addition the book consistent quantum theory by r. The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Notes on mathematics of quantum mechanics sadi turgut contents. Pdf quantum computation and quantum information, by m. An introduction, there have been tremendous strides in the field of quantum information.
In many situations that arise when studying quantum information, this framework is either inconvenient or inadequate quantum state unit vector in a hilbert space evolution unitary operators measurement projections. Iii the formalism of quantum mechanics is introduced and applied to the idea of quantum information. We give the rules for abstract hilbert spaces, so that the same rules can be applied in all speci c cases we may investigate. Vyalyi american mathematical society providence, rhode island graduate studies in mathematics. On the experimental side, the focus on the ability to manipulate and control individual quantum systems. Topological quantum computation sits at the triple juncture of quantum topology, quantum physics, and quantum computation. Solution set 1 in pdf formatmichael aaron nielsen born january 4, 1974 is a quantum physicist and. Quantum mechanics is a mathematical framework or set of rules for the construction of physical theories.
The development of quantum mechanics in its modern form spans a period of at least 2530 years between 1900 and 1930s. An introduction tony hey department of electronics and computer science, university of southampton, southampton, united kingdom so17 1bj. These examples illustrate that work at the interface of physics and information has generated noteworthy results of interest to both physicists and computer scientists. Quantum computation and quantum information by michael a. The mathematical formalism of quantum mechanics has posed new interesting problems in functional analysis, geometry, group theory today quantum information theory also o ers new mathematical challenges. The mathematical foundations of quantum mechanics springerlink.
In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum information processing investigates fascinating issues at the foundations of computer science and quantum mechanics. Information is encoded in a state of a physical system. The text book for the course will be quantum computation and quantum information by m. The measuring process and an axiomatic foundation of quantum mechanics, in foundations of quantum mechanics, il corso, academic press. The mathematical background was presented in my lectures, whereas the students were introduced to the physics of quantum mechanics in kedars part of the lecture. This is both a thorough and detailed book, and one which is very interesting and easy. Quantum particle statistics a key principle in quantum mechanics is. Quantum computation and quantum information michael a.
In contrast to this, quantum information processing involves quantum states. The book was originally published in german in 1932 by julius springer, under the. One of the goals of quantum computation and quantum information is to develop tools which sharpen our intuition about quantum mechanics, and make its predictions more transparent to human minds. This lecture will introduce quantum mechanics from a more abstract point of view than the. Chapter 1 introduction and overview caltech particle theory. Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. Quantum computation physics of information and computation are intimately related. The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and coworkers for the last three decades. Mar 16, 2000 in information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. One of the books best qualities is the remarkably logical and systematic style in which the authors present quantum information and computation systems.
Therefore, since the physical world is fundamentally quantum mechanical, the foundations of information theory and computer science should be sought in quantum physics. Quantum computation and quantum information theory course. Chuang article pdf available in contemporary physics 526. Quantum mechanics is a mathematical language, much like calculus. An important objective is to nd quantum algorithms that are signi cantly faster than any classical algorithm solving the same problem. But since mathematics is the language of nature, its required to quantify the prediction of quantum mechanics. Brain science institute, riken from 2000 to 2003, and worked in erato quantum computation and information project, japan science and technology agency jst as the research head from 2000 to 2006. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Pdf mathematical foundations of quantum information. Building qubits phase across junction energy maximum 0 energy energy minimum energy diagram of a junction electrons weak link superconductor what are the basic principles. This is the course page for quantum computation and information theory.
Revolutionary research at the intersection of computer science and quantum physics has led to a realization that computers operating according to quantum mechanics can be exponentially faster than classical computers. It may be worth reflecting that if computing with classical bits has brought about the digital era, dominated by information theory and computer science, together. Therefore, the study of information and computation are linked through a study of underlying physical processes. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. Quantum effects like interference and entanglement play no. This mathematical formalism uses mainly a part of functional analysis, especially hilbert space which is a kind of linear space. New effects involving quantum information continue to be discovered, not only in the traditional areas of computation, channel capacity, and cryptography, but in areas such as communication complexity and game theory.
The centre for quantum information and foundations, part of the university of cambridge, and based within the department for applied maths and theoretical physics, conducts theoretical research into all aspects of quantum information processing, the implications of quantum computing and quantum information theory for physics, and broader. Computation is processing of information on actual physical system that obeys certain laws. Topological quantum computation zhenghan wang microsoft research station q, cnsi bldg rm 2237, university of california, santa barbara, ca 931066105, u. The aim of the lectures was to present most of the mathematical results and concepts used in an introductory course in quantum mechanics in a. Quantum computation is the eld that investigates the computational power and other properties of computers based on quantum mechanical principles. Tqc qt qp qc the existence of topological phases of matter with nonabelian anyons would lead us to topological quantum computation via. What i would like to achieve with this course is for you to gain a deeper understanding of the structure of quantum mechanics and of some of its key points. In particular, the following topics all of which are addressed here made seen major advances. The measuring process and an axiomatic foundation of quantum mechanics, in foundations of quantum mechanics, il corso, academic press inc.
666 854 1221 475 516 759 146 85 308 1321 690 226 1260 1223 425 734 819 76 724 815 983 1176 940 69 684 290 318 717 150 158 853 743 259 989 459 403 882 781 168 1204 606 1353 558