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 6 - Quantum No-Cloning Theorem and Teleportation

  • 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 10 - The Simon Problem

  • 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 14 - Classical Information Theory

  • 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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