4803-Quantum Information, quantum computing  (year 2004)

Jean Bellissard                                                                                     Course listed jointly with
Professor of Mathematics and Physics                                                             MATH 4803BDG CRN 24293
School of Math, Skiles 132 , Physics Howey W511                                        MATH 4803BDU CRN 24286
Phone: (404) 385-2179 (Math), 404-385-2509 (Phys)                                     PHYS 4803A CRN 24576
Fax: (404) 894-4409                                                                                                  CS 4803F CRN 21345
e-mail: jeanbel@math.gatech.edu
Solution for the Problem set 4 is posted

Final !   The final exam is scheduled on
                 Friday April 30th, 11:30AM-2:30PM Room S106 Howey

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

Location and Schedule: (Spring 2004)
Howey  S106  Tuesday-Thursday 1:35-2:55PM 
From January 6th till April 2004

Course description

Quantum Mechanics is the laws of nature governing very small systems. Such systems,
like electrons, atoms, nuclear spins, photons, are liable to store and transmit information.
However, this  information does not follow the same rules as the one used in classical
systems such as modern computers or electronic devices.

The aim of the course, opened to students coming from various areas, is to introduce
them to the above mentioned notions with a minimal amount of perequisites. The following
topics will be treated:

                 Notion of qbits. Matrices, operators and quantum gates.
                 What is quantum physics ? Quantum systems used in experiments. Using linear algebra.
                 Classical and quantum  information: compression, transmission, noise, entanglement
                    cryptography, teleportation.
                 Quantum complexity: introduction, algorithm, error correcting codes.

Textbook for the course
Quantum Computation and Quantum Information
by Michael A. Nielsen, Isaac L. Chuang .
Cambridge Univ Press, (2000)

Final Exam   The final grade will be composed of :
                                         (i)   Homework (30%)

                                         (ii)  Report (20%)   (see below the list of possible topics)
                                         (iii) Final written exam (50%)

             Program :  All chapters 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 2004 in class.

Homework  Problem Set 1 (to be announced soon) due January 20, 2004  
                                  The homework will count as 30% of the final evaluation.

Report  The students are asked to choose a subject among the following list
                        A proposal (topic, plan) will be submitted by February 3, 2004, for approval.
                       The final report should contain 15-20 pages, and will be submitted by April 20, 2004, following
                       the instruction below. This report will be graded and will count for 20% of the
                       final evaluation.

                  List of topics

                 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.

                Writing the report

               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.

               Proposal submission date (by e-mail to the instructor ) Tuesday February 3rd, 2004, for approval.

               The report should be typed and accessible by e-mail or on a web site in .pdf format.
               Using LaTeX is recommanded.
               It should contain 15-20 typed pages and the following informations:
               - an expository introduction (not more than one 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....),
               - a conclusion (no more than one 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.

               Report submission date Tuesday April 20th, 2004 (.pdf format copy accessible to the instructor).

References: books, articles

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