MATH 4782, PHYS 4782, CS4803 Instructor Jean Bellissard Professor of Mathematics and Physics School of Math, Skiles 132 , Physics Howey W511 Phone: (404) 3852179 (Math), 4043852509 (Phys) Fax: (404) 8944409 email: jeanbel@math.gatech.edu 
Location Course listed jointly with 
Skiles 246 TuesdayThursday 1:352:55pm MATH 4782 BDU CRN 26671 MATH 4782 BDG CRN26670 PHYS4782 A CRN 25055 CS4803 QIC CRN 27057 
Office Hours:  Skiles 132 Tuesday 3:154:15 pm  
Dates:  January 9th till April 26th, 2007 
Topic  Text Sections  Estimated Date (2007) 
What is a qbit ? 1qbit gates, 1qbit states 
QCQI
Sections 1.2 & 2 
Jan.
911 & 1618 
Nqbits,entanglement,
Bell's inequalities 
QCQI Sections 1.3 & 2  Jan.
2325 
Controlled gates, Quantum circuits, Teleportation,  QCQI Sections 1.3 & 4  Jan.
30Feb. 1 & 68 
Fourier transform, Phase estimate Schor's algorithm  QCQI Section 5  Feb
1315 & 2022 
Quantum
Search algorithm 
QCQI Section 6  Feb.
27March 1 
Measurement, Quantum Operations  QCQI Section 8  March
68 & 1315 
Trace
distance, Fidelity 
QCQI Section 9  March
2729 
Error correction: Shor's code, CSS codes,  QCQI Sections 10.110.4  April
35 & 1012 
Error correction: Stabilizer codes  QCQI Section 10.510.6  April
1719 & 2426 
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.
Final Grade  Grade Distribution:  
Homeworks Report Final 
30% 30% 40% 
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.
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 2530
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)
Return to top
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
email 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 email or on a web
site in .pdf format.
Using LaTeX is recommended.
It should contain 2530 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
email 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
45 pages already written (to check the style).
Report submission
date Thursday
April 19th, 2007 (.pdf format copy accessible to the
instructor).
Useful Links