5 edition of Lectures on Quantum Computation, Quantum Error Correcting Codes And Information Theory found in the catalog.
November 30, 2005
by Narosa Publishing House
Written in English
|The Physical Object|
|Number of Pages||128|
The goal of this lecture is to provide architectural abstractions for the design of a quantum computer and to explore the systems-level challenges in achieving scalable, fault-tolerant quantum computation. In this lecture, we provide an engineering-oriented introduction to quantum computation with an overview of the theory behind key quantum. Developed from the author’s lecture notes, the text begins with developing a perception of classical and quantum information and chronicling the history of quantum computation and communication. It then covers classical and quantum Turing machines, error correction, the quantum circuit model of computation, and complexity classes relevant to quantum computing and s: 1.
Grassl M, Beth T () Cyclic quantum error‐correcting codes and quantum shift registers. Proc Royal Soc London A ()– MathSciNet zbMATH CrossRef Google Scholar information perfectly, then subject the qubits in our codes to noise, and then we can perfectly decode the quantum information. This model is, in some ways, ﬁne for talking about the transmission of quantum information but is.
That these codes allow indeed for quantum computations of arbitrary length is the content of the quantum threshold theorem, found by Michael Ben-Or and Dorit Aharonov, which asserts that you can correct for all errors if you concatenate quantum codes such as the CSS codes—i.e. re-encode each logical qubit by the same code again, and so on, on. Quantum Computing. / Fall Prerequisites: Understanding of linear algebra. Book: I recommend the book of Nielsen and Chuang, and will be using it to prepare some of my lectures with.
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Quantum Probability In the Mathematical Congress held at Berlin, Peter Shor presented a new algorithm for factoring numbers on a quantum computer. In this series of lectures, we shall study the areas of quantum computation (in- cluding Shor’s algorithm), quantum error correcting codes and quantum information theory.
COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.
The chapter covers three broad topics: the basic theory of quantum error-correcting codes, fault-tolerant quantum computation, and the threshold theorem. We begin by developing the basic theory of quantum error-correcting codes, which protect quantum information against noise.
The topics include a comparative description of the basic features of classical probability theory on finite sample spaces and quantum probability theory on finite dimensional complex Hilbert spaces, quantum gates and cicuits, simple examples of circuits arising from quantum teleportation, communication through EPR pairs and arithmetical.
Quantum Information Processing is a young and rapidly growing field of research at the intersection of physics, mathematics, and computer science. Its ultimate goal is to harness quantum physics to conceive -- and ultimately build -- "quantum" computers that would dramatically overtake the capabilities of today's "classical" computers.
error-correction (Chapter 14). A 15th lecture about physical implementations and general outlook was more sketchy, and I didn’t write lecture notes for it.
These chapters may also be read as a general introduction to the area of quantum computation and information from the perspective of a theoretical computer scientist. While I made an e ort. Many quantum codes can be described in terms of the stabilizer of the codewords.
The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical. Dates Subjects Lecture notes Jan.
14 Mon Course overview Jan. Review of quantum information theory I Nielsen & Chuang, Chap. 11/ Quantum error-correcting codes NC Thurs. 11/ Quantum error-correcting codes NC Tues. On quantum computation.
John Preskill's Quantum Computation course at Caltech: link. Nielsen and Chuang, Quantum Computation and Quantum Information An encyclopedic reference for quantum information theory.
weaker coverage on computational issues. Kitaev, Shen and Vyalyi, Classical and Quantum Computation Interesting but idiosyncratic.
However, recall that the phase ﬂ ipZsurrounded by twoHgates is a bit ﬂ ipX. More generally, a phase rotation surrounded by twoHgates is an amplitude rotation.
Thus a phase error is just a bit-ﬂ ip error if the code is setup to protect for bit ﬂ ips but then the qubits of the code. Lecture 4 (Jan 17): Quantum stabilizer codes Lecture 5 (Jan 22): Examples of stabilizer codes Lecture 6 (Jan 24): Cleaning lemma for stabilizer codes, quantum Gilbert-Varshamov bound Lecture 7 (Jan 29): Concatenated quantum codes, toric code Lecture 8 (Jan 31): Toric code recovery Lecture 9 (Feb 5): Existence of string operators in 2D.
A Quantum Code That Corrects Single Bit-Flip Errors A Code for Single-Qubit Phase-Flip Errors A Code for All Single-Qubit Errors The mathematical theory of quantum codes (QC) has been formulated in and developed rapidly since then.
In these lecture notes we introduce the basic concepts on QC, mathematical methods to construct good QC and some related topics. Every lecture is accompanied by readings that support and expand on what was covered in the lecture. The reference Mike & Ike refers to the book: Quantum Computation and Quantum Information: 10th Anniversary Edition, by Michael Nielsen and Isaac Chuang.
NPTEL provides E-learning through online Web and Video courses various streams. Text Book. The text book for the course will be Quantum Computation and Quantum Information by M. Nielsen and I. Chuang (Cambridge, ).
In addition the book Consistent Quantum Theory by R. Griffiths (Cambridge ) is recommended for part I of the course. Copies will be kept on reserve in the library. The book is available online here. Lectures on Mathematics Editorial Board:Ravi A. Rao (Chairperson), A.
Sankaranarayanan, Raja Sridharan Volumes are being made available for free download from this site. Missing volumes will be added in due course. Lecture 6 (Jan. 29): Concatenated codes, toric code. Handwritten lecture notes on toric code recovery, fault-tolerant recovery, fault-tolerant gates Lectures Fault-tolerant quantum memory and computation.
Lectures Quantum accuracy threshold theorem. For more details on information theory, see Wilde (also available in an arXiv version).
Other references include Information and Coding Theoryby Jones and Jones, which covers the first few classes on Information Theory, and Quantum Computation and Quantum Informationby Nielsen and Chuang, which covers most of the last two lectures on quantum error-correcting codes.
Conjecture 1: No quantum error-correction for a single qubit Conjecture 1: (No quantum error-correction): In every implementation of quantum error-correcting codes with one encoded qubit, the probability of not getting the intended qubit is at least some δ > 0, independently of the number of qubits used for encoding.
BB: Quantum Computation and Quantum Information Course bulletin board: Diderot All course announcements, discussion, lecture notes, lecture videos, and homework will be on Diderot.Quantum Information: An Introduction, Springer, J. Watrous. The Theory of Quantum Information, Cambridge University Press, Online available book.
Lecture Notes by J. Watrous. Theory of Quantum Information. Lecture Notes by J. Preskill. Quantum Computation. Lecture Notes by R. de Wolf. Quantum Computing. Entry-level Courses.Quantum information processing is the result of using the physical reality that quantum theory tells us about for the purposes of performing tasks that were previously thought impossible or infeasible.