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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: 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 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: 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 Page 1 of 6 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 Page 2 of 6 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 ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// Physical realisations Assignment – Part 3 (Hand In) 23 24 7 Apr Exam Preparation 14 Apr Exam Preparation 2007 - 2008 Vacation Exam Preparation Exam Preparation Page 3 of 6 Quantum Computing 25 26 27 28 29 30 21 Apr 28 Apr 05 May 12 May 19 May 26 May 2007 - 2008 Module Guide INDEPENDENT STUDY INDEPENDENT STUDY EXAMS Page 4 of 6 Quantum Computing Module Guide Lectures / Tutorials Mathematical Strand: Lectures: 2 lectures per week during weeks 2 – 8. Lectures take place on - 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 - 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 - 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: 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 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 Page 5 of 6 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 Page 6 of 6