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Quantum Computing
Module Guide
3COM0164 Quantum Computing
Lecturers
Joseph Spring (School of Computer Science)
Shash Virmani (School of Physics, Astronomy & Mathematics)
Module Aims and Objectives
The aims of the course are to enable students to:
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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:
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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:
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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 School of Computer Science and a quantum information
processing strand delivered by both the School of Physics, Astronomy and Mathematics and the
School of Computer Science. Commencing with the state and operator based postulates of
quantum mechanics we explore those mathematical concepts relating to the development of a
theory of quantum computation. A number of issues will be explored as the course progresses.
These will include:
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Quanta
Qubits
Superposition
Multiverse
Entanglement
Teleportation
No cloning
Interference
Error Correction
Decoherence
Complexity
Algorithms
Cryptography
The underlying mathematics commences with week 2 in preparation for the QIP strand which
begins in week 9, and will be linked into weekly practical exercises.
2007 - 2008
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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://xxx.lanl.gov
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.
2007 - 2008
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Quantum Computing
Module Guide
Module Schedule 2007/2008 (Subject to Change)
Wk # / begin
Quantum/Mathematical Strand
Introduction
– cbits and qubits;
2
01 Oct
Quantum Postulates & Related Mathematics
Groups, Rings & Fields;
Tutorial: Algebra 1
Linear Algebra: 2x2 Matrices,
Transformations, Determinants,
Tutorial: Algebra 3
Linear Algebra: Spanning Sets, GSOP,
Inner Products, Hilbert and Banach Spaces
Tutorial: From Quadratics to Complex
Numbers
Linear Algebra: Outer Products
Tutorial: Complex Numbers 2
Pauli Operators,
3
08 Oct
4
15 Oct
5
22 Oct
6
29 Oct
7
05 Nov Probability 2
8
12 Nov De Moivres Theorem,
9
19 Nov Intro to basic physical principles.
N’th Roots of Unity
Superposition
Measurement
Entanglement
Using Dirac bra-ket notation
Application of Concepts
No cloning theorem
Density operator, Partial trace
Schmidt decomposition
10
26 Nov
11
03 Dec
12
10 Dec
13
07 Jan Application of Concepts (cont’d)
Decoherence
Purification
No Lectures
14
14 Jan
15
21 Jan Unitary Operations & Quantum Gates,
Toffoli gate, Hadamard operation,
Controlled-not gate,
16
28 Jan
17
04 Feb Quantum circuits
18
11 Feb Quantum circuit applications
Reversibility
Quantum teleportation
Superdense coding
Assignment – Part 3 (Hand Out)
Error correction (decoherence)
The Deutsch-Jozsa Algorithm
19
18 Feb
20
25 Feb
21
22
03 Mar Grover’s Search Algorithm
10 Mar Shor’s Factorisation Algorithm
Mathematical/Quantum Strand
Linear Algebra: Vectors, Dirac Notation
Tutorial: Algebra 2
Linear Algebra: Linear /Vector Spaces
Tutorial: Algebra 4
Linear Algebra: Eigenvectors & Eigenvalues
Tutorial: Complex Numbers 1
Tutorial: Eigenvectors & Eigenvalues
Tutorial: Trigonometry
Probability 1
Review Algebra
Types of Operator
Spectral Decomposition Theorem
Mock Assignment 1
Linear Algebra: Trace & Exp Operator, CAR,
CCR, Polar, Singular Value Decomposition
Review Mock Assignment 1
Tensor Products, Entanglement,
Assignment – Part 1 (Test)
Circuits and Turing Machines 1
Vacation
Circuits and Turing Machines 2
Assignment – Part 2 (Hand Out)
No Lectures
Asymptotic Notation / Complexity 1
Tutorial: Asymptotic Notation / Complexity 1
Asymptotic Notation / Complexity 2
Tutorial: Asymptotic Notation / Complexity 2
Classical Cryptography , Unconditional &
Computational Security
Quantum Cryptography, Quantum Key Exchange
QKE: Examples / Quantum Probability /
Quantum Voting
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Physical realisations
Assignment – Part 3 (Hand In)
23
24
7 Apr Exam Preparation
14 Apr Exam Preparation
2007 - 2008
Vacation
Exam Preparation
Exam Preparation
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Quantum Computing
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21 Apr
28 Apr
05 May
12 May
19 May
26 May
2007 - 2008
Module Guide
INDEPENDENT STUDY
INDEPENDENT STUDY
EXAMS
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Quantum Computing
Module Guide
Lectures / Tutorials
Mathematical Strand:
Lectures: 2 lectures per week during weeks 2 – 8. Lectures take place on
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Monday morning from 11:00 to 12:00 in Room C154
Thursday evening from 17:00 to 18:00 in Room TBA
Lectures/Tutorials: 2 per week during weeks 2 – 8. Lectures/tutorials take place every
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Monday afternoon from 12:00pm to 13:00pm in Room C154
Thursday evening from 18:00 to 19:00 in Room TBA
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).
From weeks 9 – 13 the mathematical strand will be delivered during the Monday sessions only.
Exam Preparation will be delivered as indicated in the module schedule given above.
Quantum Strand:
Lectures: 1 lecture per week
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Lectures take place on Thursday evenings from 17:00 to 19:00 in Room TBA as
indicated in the module schedule above.
Module Assessment
The module will be assessed in two ways:
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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 or
recommended to students. It will be based upon the material delivered in both the
mathematical and quantum strands of the course
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An in-module assessment consisting of three parts. Part 1 is from the Mathematical
strand of the course. It is a closed book test based on the work covered in Algebra,
Complex Numbers, Probability and Vectors. Part 1 is worth 10 % of the total module
assessment. Part 2 is a research based assignment relating to a topic that may be viewed
from both a classical and quantum perspective. Part 2 is worth 20 % of the total module
assessment. Part 3 is based on the Quantum strand of the course. Part 3 is worth 20 %
of the total module assessment.
Students will need to gain a pass overall in order to pass this module.
Feedback
The in-module assessment should give you feedback on your progress. In addition questions
will be posed to be considered prior each lecture, which should help you to identify areas that
you need to mug up on. Tutorial sessions and material will also be set. These will give you feed
back on your progress for the mathematical strand of the course.
2007 - 2008
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Quantum Computing
Module Guide
The mathematical strand of this course will have up to ½ hour (after the lecture) to discuss
problems that have arisen from either the mathematical or quantum strand of the course. The
mathematics lecturer will be available for the timetabled 50 minute slot.
Further tutorials can be arranged on a 1-1 or small group basis by arrangement.
(email: [email protected] )
StudyNET
We will use StudyNet for some electronic course materials 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
Shash Virmani
2007 - 2008
Room
LC267
TBA
E-Mail
[email protected]
[email protected]
Telephone
4351
tba
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