Updated March 20, 2008; Email: spp@cse.iitkgp.ernet.in

This course has no prerequisites and the necessary background in linear algebra, algebra and quantum mechanics will be included in this self-contained first level course.

Undergrads in their second and third year (B Tech and M Sc) must meet their respective faculty advisors to register for this course, possibly treating it as an additional elective, if not as a breadth elective.

For 10th semester Dual degree (CSE) and 8th semester B. Techs (CSE), this is an elective in the regular elective list in slot B.

For UGs from other departments and dual degree students, this course can be a breadth elective.

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Registrants (Creditors)

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Vinayak Pathak (3rd year B Tech CSE 05CS1027), Mridul Aanjaneya (4th (final) year B Tech CSE ), Manoj Payardha (B Tech CSE 03CS1029), Ujjwal Sarkar (M Tech 1st year 07CS6033), S. Vinith Kumar Reddy (M Tech 1st year 07CS6018)

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Syllabus:

Mathematical foundations; quantum mechanical principles and concepts; qubits, quantum entanglement; reversible computation, quantum gates and registers; universal gates for quantum computation; quantum parallelism and simple quantum algorithms; quantum Fourier transforms and its applications, quantum search algorithms; elements of quantum automata and quantum complexity theory; introduction to quantum error correcting codes; entanglement assisted communication; elements of quantum information theory and quantum cryptography.

------------ Main texts:

(0) M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.

(1) Jozef Gruska, Quantum Computing, McGraw Hill, 1999.

----------- References:

(00) Lecture notes by John Preskill. http://www.theory.caltech.edu/people/preskill/ph229/

(01) Lecture Notes by N. D. Mermin. http://people.ccmr.cornell.edu/~mermin/qcomp/CS483.html

(02) Chris. J. Isham, Lectures on Quantum Theory: Mathematical and Structural Foundations, Imperial College Press, 1995

(03) D. Bouwmeester, A. Ekert and A. Zeilinger, editors, The Physics of Quantum Information, Springer, 2000

(04) H.-K. Lo, S. Popesku and T. Spiller, Editors, Introduction to Quantum Computation and Information, World Scientific, 1998

(05) M. D. Srinivas, Measurements and Quantum Probabilities, Universities Press (India), 2001

(06) I. N. Herstein, Topics in Algebra, 2nd Edition, John Wiley and Sons, 1999

(07) E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley and Sons, 1978

(08) R. Bhatia, Matrix Analysis, Springer, 1997

(09) Paul R. Halmos, Finite dimensional vector spaces, Princeton Univ. Press.

(10) Bela Bollobas, Linear Analysis, Cambridge University Press, 1990.

(11) Los Alamos Quant_ph archive. http://www.arxiv.org/archive/quant-ph

(12) T. H. Cormen, C. E. Leiserson and R. L. Rivest, Introduction to Algorithms, MIT Press (1990)

(13) Mika Hirvensalo, Quantum Computing, second Edition, Springer, 2004.

(14) Arthur O. Pittenger, An introduction to quantum computing algorithms, Birkhauser, Progress in Computer Science and Applied Logic, 2001.

(15) Sakurai, Modern quantum physics.

(16) Approaching Quantum Computing by Marinescu and Marinescu.

(17) Vishal Sahni, Quantum Computing, Tata-McGraw Hill.

(18) Introduction to Hilbert Spaces with Applications, Lokenat Debnath and Piotr Mikusinski. ==================================================================

Selected lectures' summary

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Jan 07, 2008

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Introduction to quantum states, qubits, quantum parallelism, Pauli operators, and tensor notation/products.

Jan 08, 2008

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The Stern-Gerlach experiment and its quantum interpretation. Deustch's problem for a single-bit boolean function; the use of Hadamard operators and spawning superpositions.

Jan 10, 2008

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Quantum parallelism and the Bernstein-Vazirani problems; the use of Hadamard operators, spawning an exponential number of states, and rudimentary phase estimation.

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January 14, 2008 Monday

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Inner product space, Hilbert space, tensor product, quantum measurement, spectral decomposition of a Hermitian operator

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January 15, 2008 Tuesday

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Properties of H, X, Y, Z operators, introduction to basis vectors and subspaces, n-qubit systems, quantum entanglement.

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January 17, 2008 Thursday

Tutorial:

January 21, 2008 Monday

Quantum teleportation, universal quantum gates

January 22 , 2008 Tuesday

Introduction to linear operators; Description of double-slit experiment and quantum mechanical explanation, measurements, observables, quantum teleportation (revisted)

January 24, 2008 Thursday

Elements of quantum parallelism, evolution of quantum system --- brief discussion of Schrodinger's wave equation; Simon's problem

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Lecture notes

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