QUANTUM INFORMATION AND COMPUTING
Course Outline
Topics covered in this course are
Classical information theory, Shannon’s noiseless coding theorem and entropy.
Review of quantum mechanical formalism, Qubits, Bloch sphere representation, Quantum parallelism, Generalized measurements, Density operators, EPR and Bell’s inequalities. Entanglement. Bell’s theorem. Von Neumann entropy.
Quantum data compression.
Quantum gates and circuits, Simple quantum algorithms – Deutsch problem, Bernstein-Vazirani problem, Simon’s problem. Quantum Fourier transform, Order finding and Shor’s algorithm.
Database search using a quantum computer, the Grover algorithm. Quantum cryptography.
Course Books
** Michael A. Nielsen and Issac L. Chuang , “Quantum Computation and Quantum Information”, Cambridge, University Press, 4th Asian Edn., 2002.
N. D. Mermin, “Quantum Computer Science – An Introduction”, Cambridge University Press, 2007.
Mikio Nakahara and Tetsuo Ohimi, Quantum Computing (From Linear Algebra to Physical Realizations), CRC Press, 2008
** Primary Text
Web Reference :
Lecture Notes by John Preskill
Course Lecture Notes
Topic 1 - Classical Information Theory : The lecture introduces the elements of classical information theory. Shannon entropy is defined and the principle of uniquely decipherable codes discussed.
Topic 2 - Quantum Computing - I : The lecture starts with a review of Quantum Mechanics and its postulates, Defines a qubit and its representation on a Bloch sphere. Some essential results of linear algebra are reviewed.
Topic 3 - Quantum Computing - II : Density matrix, mixed states and their Bloch sphere representation, Reduced Density matrix
Topic 4 - Multiqubit states, Quantum Gates and Circuits
Topic 5 - Quantum Circuits
Topic 7 - Super Dense Coding
Topic 8 - Measurement Theory - I, von-Neumann measurement, POVM, Measurement Theory - II, CPTP Map, Kraus operators, Amplitude damping channel, Depolarizing channel.
Topic 9 - Simple Quantum Algorithms - Deutsch Algorithm, Deutsch-Jozsa Algorithm, Bernstein-Vazirani Algorithm.
Topic 11 Grover's Search Algorithm
Topic 12 - Discrete Integral Transform, Quantum Fourier Transformand its implementation
Topic 13 - Shor's Factorization Algorithm - Period Finding and implementation, method of continued fraction
Topic 15 - Shannon Entropy, Gibb’s Inequality, Kraft Inequality, Shannon's Noiseless Coding Theorem
Topic-16 - Von-Neumann Entropy, Review of Shannon Entropy, Jensen’s Inequality, Quantum Relative Entropy, Sub-additivity, Concavity of von- Neumann entropy
Topic 17 - EPR and Bell's Inequalities, Wigner formulation of Bell’s inequalities, Venn diagram, CHSH Inequality, Alian Aspect’s experimental verification.
Topic 18 - RSA Algorithm - Fermat's Little Theorem, Chinese Remainder Theorem, RSA Encryption and Decryption
Topic 19 - Quantum Cryptography : BB-84 protocol, B-92 protocol and Eckert- 91 protocol.
Topic 20 - Error handling in quantum communication, Three qubit code, Shor's 9 qubit code.
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