Course description Prerequisites:
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
Quantum complexity: introduction, algorithm, error correcting codes.
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).
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