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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 Page 1 of 5 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 Page 2 of 5 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 ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// 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 Page 3 of 5 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 Page 4 of 5 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 Page 5 of 5