Quantum Computing

IT 853 – Elective 4 (Choice 3) – QUANTUM COMPUTING [40 Lectures]

Learning Objective: According to Gordon Moore, the dream run of computer hardware development had to end because conventional approaches to the fabrication of computer technology are beginning to run up against fundamental difficulties in size. Quantum effects are beginning to interfere in the functioning of electronic devices as they are made smaller and smaller. The field of quantum computing started in the early 1980s with suggestions by Paul Benioff and Richard Feynman and reached the more rigorous ground when in 1985 David Deutsch defined the universal quantum Turing machine. Since then rapid advances in quantum algorithms and quantum system design is increasing the attraction for quantum computing in recent years. In the case of solving certain important problems quantum computer significantly outperforms the classical computer. This course equips a student with basic knowledge of quantum information theory, quantum algorithms which exploit different quantum mechanical phenomena like superposition, entanglement etc. and circuit synthesis along with quantum error correction. At the end of the course, the student should have a clear idea of some basic algorithms and they might build upon them to create a more efficient solution for different problems.

1. Introduction to Hilbert Space: [6 lectures]

Linear vector space, scalar product, eigenvalue and eigenvectors, self-adjoint operators, unitary operators, projection operators, spectral decomposition, tensor product.

2. Basic Introduction to Quantum Mechanics: [8 lectures]

(i) Postulates of quantum mechanics, uncertainty principle, unitary dynamics, two-level quantum system. (ii) Multipartite quantum systems, quantum entanglement, Schmidt decomposition, Density operator. (iii) No-cloning theorem, Kraus operators.

3. Basic Quantum Information Processing: [6 lectures]

(i) Quantum Dense Coding, (ii) Quantum Teleportation, (iii) Remote State Preparation, (iv) Quantum Key Distribution .

4. Basic Quantum Circuit: [6 lectures]

(i) Circuit model of computation, Reversible computing, Reversible to quantum circuits. (ii) Quantum gates – Walsh-Hadamard transform, SWAP, CNOT, FREDKIN gates, Basic quantum circuits.

5. Quantum Algorithms: [8 lectures]

Quantum Parallelism, Deutschs algorithm, Deutsch-Jozsa algorithm, Simons algorithm, Grovers’ search algorithm, Quantum Fourier Transform and Shor’s factoring algorithm, Elementary idea of Quantum Random Walk.

6. Quantum Error Correction: [6 lectures]

Linear Quantum error correcting codes - Shor code, Steane code, Laflamme code and corresponding Stabilizer structures. Topological codes.

Reference Books:

1. Quantum Computation and Quantum Information, Michael A. Nielsen and Isaac L. Chuang, Cambridge University Press, 2002.

2. From Classical to Quantum Shannon Theory, Mark M. Wilde, arXiv: 1106.1445 [quant-ph]

3. An Introduction to Quantum Computing, Phillip Kaye, Raymond Laflamme, and Michele Mosca. Oxford U. Press, New York, 2007.

4. Quantum Computing, Jozef Gruska, McGraw-Hill, 1999.

5. Quantum Computing Explained David McMahon, Wiley-IEEE Computer Society Press, March, 2007