Syllabus
- Introduction: Quantum states, density operators, generalized measurements, quantum operations/channels, no-cloning theorem.
- Quantum correlations: Bell inequalities and entanglement, Schmidt decomposition, super-dense coding, teleportation, PPT criterion.
- Quantum gates and algorithms: Universal set of gates, quantum circuits, Solovay-Kitaev theorem, Deutsch-Jozsa algorithm, period-finding, factoring, Shor's algorithm, quantum search, Abelian quantum hidden subgroup problem.
- Quantum information theory: Shannon entropy, noiseless coding theorem, von Neumann entropy and properties, Schumacher compression, noisy-coding theorem.
- Quantum cryptography: quantum key distribution, entropic uncertainty relations
- Quantum noise and error-correction: Distance measures, Knill-Laflamme conditions, quantum error-correcting codes, Hamming bound
Text-books
(1) Quantum Computation and Quantum Information, M. A. Nielsen & I.Chuang, Cambridge University Press (2000).
(2) Lecture notes by Prof. John Preskill, California Institute of Technology
References
(1) The mathematical language of quantum theory: from uncertainty to entanglement, T. Hienosaari & M. Ziman, Cambridge University Press (2011).
(2) Quantum systems, channels, information, A.S. Holevo, de Gruyter Studies in Mathematical Physics (2012).
(3) Quantum information Theory, Mark M. Wilde, Cambridge University Press (2012).
(4) Quantum error correction, D. A. Lidar & T. A. Brun, Cambridge University Press (2013).
Grading format: Assignments - 25%, Mid-semester exam - 20%, End-semester exam - 55%
Lecture Notes:
Introduction
Week 1 (31 Jul - 4 Aug) : Qubits, Bloch Sphere, Quantum Parallelism : Deutsch Algorithm.
Extra reading: Feynman's classic article on "Simulating physics with computers" ; Preskill's recent article titled "Can we exploit the wierdness of quantum mechanics?" .
Week 2 (7, 10 Aug) : The no-cloning principle; Composite Systems: Bell States, Teleportation.
Reference: "A single quantum cannot be cloned", Wootters and Zurek, Nature 299, 802 (1982). [link]
Week 2 (11 Aug): Review of Quantum Mechanics; Outer-product, Linear Operators, Projective Measurement.
Week 3 (14,17 Aug) :
POVM, Non-orthogonal quantum states cannot be distinguished.
Assignment 1 (Due: 28 August)
Weeks 3-4 (18,24 Aug) : Density Operator, SHJW Theorem .
Week 5 (28,31 Aug) : Qubit density operator; Partial trace & reduced density operator.
Week 5 (1 Sep) : Entanglement : Super-dense coding; Schmidt decomposition.
Week 6 (4 Sep) : Singular Value Decomposition, Schmidt rank, Entropy, Purification.
Assignment 2 (Due: 14 September)
Week 6 (7 Sep) : Bell-CHSH Inequality.
Week 7 (11,15,18 Sep) : Mixed state entanglement: PPT criterion; Multipartite entanglement.
Quantum Gates, Circuits and Algorithms
Week 8(21,22 Sep): Classical Ciruit Model, Complexity Classes.