Download 3COM0074 Quantum Computing - Department of Computer Science

Quantum Computing
Module Guide
3COM0074 Quantum Computing
Lecturers
Joseph Spring (Department of Computer Science)
Susana Huelga (Department of Physical Sciences)
Module Aims and Objectives
The aims of the course are to enable students to:
?? Appreciate the fundamental principles involved in Quantum Computing
?? Appreciate how the issues and concerns in classical computing are modified when
extended to Quantum Computing
?? Acquire a framework for understanding the concepts involved in Quantum Computing
?? Appreciate the importance and limitations of techniques employed
On successful completion of this module you will have a knowledge and understanding of:
?? The fundamental concepts in Quantum Computing
?? The underlying mathematical structure used in Quantum Computing
?? A selection of applications within the field of Quantum Computing
Successful students will also be able to:
?? Identify and evaluate a selection of key concepts to Quantum Computing
?? Select and deploy appropriate techniques to applications of Quantum Computing
Module Overview
The course develops a two-strand approach to Quantum Computing, with an underlying
mathematical strand delivered by the Department of Computer Science and a quantum
information processing strand delivered by the Department of Physical Sciences. Starting from
the postulates for quantum mechanics we explore the motivation for development in this area
and open up a number of issues that to be explored later in more depth. These will include:
?? Quanta
?? Qubits
?? Superposition
?? Multiverse
?? Entanglement
?? No cloning
?? Interference
?? Error Correction/Decoherence
?? Parallelism
?? Teleportation
?? Cryptography
?? Quantum Algorithms
The underlying mathematics will also commence in week 2 in preparation for the QIP strand
which begins in week 9, and will be linked into weekly practical exercises.
2003 - 2004
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Quantum Computing
Module Guide
Module Pre-Requisites
A minimum of a grade C GCSE in Mathematics at the intermediate level (or its equivalent) is
required. Students should expect an active rather than passive experience throughout the
course
Reading and Other Resources
The recommended reading for this course is:
Nielson and Chuang, Quantum Computation and Quantum Information,
Cambridge University Press, 2002 (ISBN 0-521-63503-9)
You might find the following useful as background reading:
Roger Penrose, Shadows of the Mind, Vintage, 1995 (ISBN 0-09-958211-2)
Julian Brown, Minds, Machines and the Multiverse – The Quest for the Quantum
Computer, Simon & Schuster, 2000 (ISBN 0-684-81481-1)
Other texts that you might find useful include:
Jozef Gruska, Quantum Computing, McGraw-Hill, 1999 (ISBN 0-07709-503-0)
Mika Hirvensalo, Quantum Computing, Springer, 2001 (ISBN 3-540-66783-0)
Gennady Berman et al; Introduction to Quantum Computers, World Scientific, 1998
(ISBN 981-02-3490-2)
Dirk Bouwmeester, Artur Ekert, Anton Zeilinger (Eds.), The Physics of Quantum
Information, Springer, 2000 (ISBN 3-540-66778-4)
Byron and Fuller, Mathematics of Classical and Quantum Physics, Dover, 1992 (ISBN
0-486-67164-X)
This is by no means an exhaustive list – there are many texts on QC related topics. If we
discover others which we think are particularly good, we’ll let you know.
The Internet provides a useful source of information. Here are some useful QC related web
sites:
http://www.qubit.org/
http://www.simonsays.com/excerpt.cfm?isbn=0684814811
http://searchhp.techtarget.com/sDefinition/0,,sid6_gci332254,00.html
http://researchweb.watson.ibm.comquantuminfo/
http://www.iro.umontreal.ca/~paquin/Qu/quantum.html
http://www.tamagawa.ac.ip/SISETU/GAKUJUTU/pderc/rqcs/engish/e -index.html
http://qso.lanl.gov/qc/
http://209.157.184.133/qci/
http://fenyman.media.mit.edu/quanta/nmrqc-darpa/index.html
http://www.nd.edu/~qcahome /
http://www.icscusa.com/
http://www,icap2000.de
http://Socrates.Berkley.edu/~dabacon/index.html
We will advise you if we think it useful or helpful for you to consult other texts.
2003 - 2004
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Quantum Computing
Module Guide
Module Schedule 2002/2003 (Subject to change)
Wk # / begin
Quantum Strand
Mathematical Strand
2
29 Sep
3
06 Oct Introduction, Quantum Postulates & Underlying Mathematics
4
13 Oct Algebra 1 – 4, Complex Numbers 1, Radians, Arc length, Trig and Exponential
Functions & Probability 1
5
20 Oct /////////////////////////////////////////////////////////
6
27 Oct /////////////////////////////////////////////////////////
7
8
9
03 Nov /////////////////////////////////////////////////////////
10 Nov /////////////////////////////////////////////////////////
17 Nov Intro to basic physical principles.
10
24 Nov
Superposition
Measurement
Entanglement
Using Dirac bra -ket notation
11
01 Dec Application of Concepts
12
08 Dec
Linear Spaces 1 – Vectors
Operator Theory 1 – Matrices, bra-kets
Linear Spaces 2 – Metrics, Inner
Products & Hilbert Spaces
Assignment Part 1 – Algebra Test 10%
Linear Algebra 3 – Eigen vectors/values
Linear Algebra 3 – Tensor Products
Grounding Abstract Concepts
Trig Identities, Spherical Coordinates &
The Bloch Sphere
Complexity Theory 1
Assignment Part 2 – Issued
Co mplexity Theory 2
No cloning theorem
Density operator, Partial trace
Schmidt decomposition
Vacation
13
14
15
16
17
18
12 Jan Application of Concepts (cont’d)
Decoherence
Purification
19 Jan Unitary Operations & Quantum Gates
26 Jan Hadamard operation
02 Feb Controlled-not gate
Toffoli gate
Quantum circuits
Reversibility
09 Feb Quantum circuit applications
Quantum teleportation
16 Feb Superdense coding
Error correction (decoherence)
Complexity Theory 3
Complexity Theory 4
No Lectures – Submit Assignment Part 2
Groups, Rings, Integral Domains &
Fields
Discrete Fourier Transform
Heisenberg Uncertainty Principle
Superposition v Multiverse
Youngs Slit, Schrodingers cat
Quantum Cryptography 1
Quantum Cryptography 2
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19
20
21
22
23
24
23 Feb
01 Mar
08 Mar
15 Mar
22 Mar
29 Mar
25
26
27
26 Apr ////////////////////////////////////////////////////////
Revision
03 May Revision
/////////////////////////////////////////////////////////
10 May
INDEPENDENT STUDY
The Deutsch-Jozsa Algorithm
Grover’s Search Algorithm
Shor’s Factorisation Algorithm
Physical realisations
Vacation
EXAMS
2003 - 2004
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Quantum Computing
Module Guide
Lectures
For the weeks as indicated in the table above
Mathematical Strand:
Lectures: 1 lecture per week
-
Lectures take place every Monday morning from 9:00am to 10:00am in Room A450
Tutorials: 1 tutorial per week
-
Tutorial take place every Monday morning from 10:00am to 11:00am in Room A450
Handouts will usually be available at lectures, but in order to cut down on paper, we will also
be posting copies of slides and any other handouts that we produce on the module web site (see
below for details).
Quantum Strand:
Lectures: 1 lecture per week
-
Every Thursday from 3:00pm to 5:00pm in Room 1F392
Module Assessment
The module will be assessed in two ways:
?? A written examination worth 50% of the total module assessment. This will be based
on an understanding of the lecture notes, set book and any journal papers issued to
students. It will be based upon the material delivered in both the mathematical and
quantum strands of the course
?? Two in-module assessments each worth 20% of the total module assessment. One
from the Mathematical Strand. The other from the Quantum strand. In addition an
algebra assessment worth 10%.
Students will need to obtain a combined pass mark (from the written examination and the
combined in-module assessments) in order to pass this module.
Feedback
The three in-module assessments should give you feedback on your progress. In addition I will
be posing questions to be considered during preparatory readings before each lecture, which
should help you to identify areas that you need to mug up on. Together with each lecture there
will be tutorial sessions. These will give you week by week feed back on your progress with
the mathematical strand of the course.
The mathematical strand of this course will have an additional ½ hour set aside each week (at
9:00am prior to the Monday morning lecture ) to discuss problems that have arisen from either
the mathematical or quantum strand of the course.
Further tutorials can be arranged on a 1-1 or small group basis by arrangement.
2003 - 2004
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Quantum Computing
Module Guide
(email: [email protected] )
StudyNET
We will use StudyNet for electronic course materials (e.g. Lecture Slides) and as a forum for
discussion and general feedback. We will also use StudyNET for stop press announcements.
You will have to be registered on the Quantum Computing Course (module) on StudyNET to
access this medium. Log unto StudyNET using the following URL:
http://www.studynet.herts.ac.uk/
Module Web Site
The mathematical strand of the course has its own web page (URL:
http://homepages.feis.herts.ac.uk/~comqjs1) where you can see the course schedule and
description, and copies of slides and other handouts. Once you obtain the above site follow the
link for Quantum Computing. The site will also contain links to other QC related web sites. I
will use this web site, as well as StudyNet, to post any stop press announcements.
Contacts
Module Lecturers
Name
Joseph Spring
Susana Huelga
2003 - 2004
Room
LC267
1E112B
E-Mail
j.spring
s.f.huelga
Phone
4351
3599
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