4803-Quantum Information, quantum computing  (Spring 2005)

Jean Bellissard                                                                                     Course listed jointly with
Professor of Mathematics and Physics                                                             MATH 4803BDG CRN 24053
School of Math, Skiles 132 , Physics Howey W511                                        MATH 4803BDU CRN 24058
Phone: (404) 385-2179 (Math), 404-385-2509 (Phys)                                     PHYS 4803A CRN 24277
Fax: (404) 894-4409                                                                                                  CS 4803QIC CRN 21285
e-mail: jeanbel@math.gatech.edu
Final Exam:  Monday May 2nd,
11:00am-2:00pm room 246


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

Location and Schedule: (Spring 2005)
Skyles  246  Tuesday-Thursday 1:35-2:55PM 
From January 11th till April 2005

  Homework for the week  

  Course description

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

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
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. The following
topics will be treated:

                Notion of qbits. Matrices, operators and quantum gates.
                Quantum circuits & algorithms: teleportation, Fourier transform, Schor algorithm.
                 Elements of quantum physics: quantum systems used for computing.
                 Measurement & quantum operations.
                 Error correcting codes.

For an overview see
Two Lectures  on
"Quantum Computing"
        "I: Introduction. Qubits, Quantum circuits (pdf) "
                                      (PowerPoint version 0.4MB)
        "II: Algorithms, Error-correcting codes, Physical Realizations (pdf)"
                                      (PowerPoint version 0.7MB)

given at Georgia Institute of Technology,
School of Mathematics, Atlanta, GA, October 15 & 29,  2003

  Final Exam   1st week of May.
                                       The final grade will be made 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 2005 in class.

   Homework  The homework will count as 30% of the final evaluation.
Find the homework of the week here !!

  Report  The students are asked to choose a subject among the following list
                       A proposal (topic, plan) will be submitted by February 3, 2005, for approval.
                       A progress report will be submitted on March 8th, 2005,
                       The final report should contain 15-20 pages, and will be submitted by April 21, 2005, following
                       the instructions below. This report will be graded and will count for 20% of the
                       final evaluation.

                  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.

                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 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 3rd, 2005, 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

               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 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....), showing that
                 the student has mastered technics taught in class.

               - 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.

               Progress report: submission date (.pdf file by e-mail to the instructor ) Tuesday March 8th, 2005, 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 21st, 2005 (.pdf format copy accessible to the instructor).

  References: books, articles

  Useful Links