4782-Quantum Information, quantum computing  (Spring 2007)

MATH 2401 and familiarity with matrix calculus and finite dimensional vector spaces.

Textbooks

Quantum Computation and Quantum Information  (QCQI) by Michael A. Nielsen, Isaac L. Chuang . Cambridge Univ Press, (2000)

Homework

Students will be required to turn in a series of homework periodically. Please check the web page. These homeworks will be graded and will count in the final grade.

             Program :    All Sections, except Sections 7 & 11, of the Book
                                     Quantum Computation and Quantum Information
                                     (by Michael A. Nielsen, Isaac L. Chuang . Cambridge Univ Press, (2000) )
                                     that will be treated during the Spring semester 2007 in class.

  Course description
Quantum Mechanics is the law of nature governing very small systems. Such systems,
like electrons, atoms, nuclear spins, photons, are liable to store and transmit information.
Such small quantum systems do not couple easily to the rest of the world, so that they evolve with
no loss of information as long as no measurement is made on them. It is thus, in principle, possible treated
to make such a system compute for us, much faster than any available computer and have the loss of
information only at the very end, while retrieving the result.

The aim of the course, opened to students coming from various areas, is to introduce
them to quantum computing with a minimal amount of perequisites.

By lack of time, the content of the course, however will not treat fully some important aspects of
quantum computing such as physical realizations, (QCQI Section 7) or quantum information theory
(QCQI Section 11) which will only be introduced  and superficially developed.

  Report  The students are asked to choose a subject among the following list
                       A proposal (topic, plan) will be submitted by February 8th, 2007, for approval.
                       A progress report will be submitted on March 15th, 2007,
                       The final report should contain 25-30 pages, and will be submitted by April 19th, 2007, following
                       the instructions below. This report will be graded and will count for 20% of the
                       final evaluation.
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                  List of topics (non exhaustive)

                 Qubits builts from quantum dots,
                 The "Quantronium": a Josephson junction qubit,
                 Controlled entanglement: physical realization,
                 Quantum computing with ion traps,
                 Quantum computing with NMR,
                 Quantum computing with photons,
                 Quantum computing with microwaves,
                 Can one quantum compute with excitons ?
                 Quantum cryptography: theory and applications,
                 Kitaev's topological quantum computing,
                 Algorithms: quantum search, quantum simulation, quantum counting   
                 Decoherence: definition, examples, dissipation, mathematical description.
                 Error correcting codes,
                 Quantum versions of the Shannon theorem,
                 Quantum chaos as a possible limit to quantum computing,
                 Quantum noise: quantum corrections to Shottky theory of shot noise, experiments.
                 Classical logic and quantum computing: the Goedel theorem. 
                 Quantum information theory.
                 Building a quantum computer: the Steane project (December 2004)
                 Storing a photon state in a memory (Kuzmich team experiment December 2005)
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                Writing the report (see the Mayfield Handbook of Scientific Writing)

               The student will choose a topic among this list or make his own choice (with the approval
               of the instructor). He will also choose one or two papers (or a book chapter) to read
               as an illustration of this subject and collect documents that may help understanding these papers

               Proposal submission date (.pdf file to be sent by e-mail to the instructor ) Thursday February 8th, 2007, for approval
               The proposal should be presented on 1/2 a page in .pdf format, containing
               (i) the title (ii) a list of possible sections organizing the report (iii) a list of documents to start with
               together with their exact and complete reference

               Content of the report The report should be typed and accessible by e-mail or on a web site in .pdf format.
               Using LaTeX is recommended.
               It should contain 25-30 typed pages and the following informations:
               - an expository introduction (not more than two typed page) explaining the motivation,
                 the purpose and the history of the topic,
               - a section describing the content of the paper that has been read. This part should contain at least
                 one technical aspect (calculation, experiment, computer simulation, or algorithm....), showing that
                 the student has mastered technics taught in class.
               - a conclusion (no more than two page) giving a clear description of the outcome for this topics,
                 its limitation, its future,
               - a list of references: only those references effectively looked at by the student should be quoted;
                 a special attention will be paid upon how the references are quoted (exact location, standard),
                 web sites references can be used if properly quoted.

               Progress report: submission date (.pdf file by e-mail to the instructor ) Thursday March 15th, 2007, Students
               will give an account of what they have done so far: list of documents collected, an updated outline and
               4-5 pages already written (to check the style).

               Report submission date Thursday April 19th, 2007 (.pdf format copy accessible to the instructor).

  References: books, articles

  Useful Links
 
 

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