4782-Quantum Information, quantum computing  (Spring 2006)

 MATH 4782, PHYS 4782, CS4803
Jean Bellissard
Professor of Mathematics and Physics
School of Math, Skiles 132 , Physics Howey W511

Phone: (404) 385-2179 (Math), 404-385-2509 (Phys)
Fax: (404) 894-4409
e-mail: jeanbel@math.gatech.edu

Course listed
jointly with
Howey Physics S104  Tuesday-Thursday 1:35-2:55pm

MATH 4782 BDU CRN 27249
MATH 4782 BDG  CRN27248
PHYS4782 A CRN 27646
CS4803 QIC  CRN 27648

Office Hours: Skiles  132  Tuesday 3:15-4:15 pm

Dates: January 10th till April 27th, 2006

Update : Final Report is due on Tuesday April 18th, 2006
                Homework #3 due on Thursday April 20th 2006
                Correction of Homework #2 is online

  Homework for the week: due date on Thursday April 20, 2006

Course Outline
Topic Text Sections Estimated Date (2006)

What is a qbit ? 1-qbit gates, 1-qbit states

QCQI Sections 1.2 & 2
Jan. 10-12 & 17-18
N-qbits,entanglement, Bell's inequalities 
QCQI Sections 1.3 & 2 Jan. 24-26
Controlled gates, Quantum circuits, Teleportation, QCQI Sections 1.3 & 4 Jan. 31-Feb. 2 & 7-9
Fourier transform, Phase estimate Schor's algorithm QCQI Section 5 Feb 14-16 & 21-23
Quantum Search algorithm
QCQI Section 6 Feb. 28-March 2
Measurement, Quantum Operations QCQI Section 8 March 7-9 & 14-16
Trace distance, Fidelity
QCQI Section 9 March 28-30
Error correction: Shor's code, CSS codes,  QCQI Sections 10.1-10.4 April 4-6 & 11-13
Error correction: Stabilizer codes QCQI Section 10.5-10.6 April 18-20 & 25-27

  Important Deadlines:
     - Thursday  February 2nd 2006:
submit your report plan

     - Thursday  March 9th 2006:
submit your progress report

     - Tuesday  April 18th 2006:
submit your report by e-mail as a 30 pages .pdf file

     - Tuesday  May 2nd 2006: 
Final Exam


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


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

Final Exam  May 2nd 2006

             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 2006 in class.

Final Grade

Grade Distribution:




90% for an A
80% for a   B
70% for a   C
60% for a   D

  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.

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)

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

  Report  The students are asked to choose a subject among the following list
                       A proposal (topic, plan) will be submitted by February 2, 2006, for approval.
                       A progress report will be submitted on March 9th, 2006,
                       The final report should contain 25-30 pages, and will be submitted by April 18, 2006, 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 2nd, 2006, 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 9th, 2006, 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 Tuesday April 18th, 2006 (.pdf format copy accessible to the instructor).

  References: books, articles

  Useful Links

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