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: Assignment Quiz - 20%, Mid-semester exam - 20%, Term Paper - 20%, End-semester exam - 40%
Lecture Notes:
Introduction
3 Aug: Introducing 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?" .
6 Aug: Fundamentals: Quantum States and Operators, The no-cloning principle .
Reference: "A single quantum cannot be cloned", Wootters and Zurek, Nature 299, 802 (1982). [link]
7,10 Aug: Quantum Measurements: Projections and POVMs; Non-orthogonal quantum states cannot be distinguished.
13,14 Aug: Density Operator: SHJW Theorem
Quantum Correlations
17,20 Aug: Composite systems: Bell States, Teleportation, Reduced density operator (partial trace)
21 Aug: Super-dense coding, Schmidt decompostion
27 Aug: Special Lecture by Prof. Sunder on Singular Value Decomposition [Handwritten notes, courtesy Maria Quadeer: Part 1, Part 2, Part 3, Part 4]
31 Aug: SVD, Schmidt decomposition, purification
3 Sep: Bell-CHSH inequality
Extra reading: A recent experimental violation of the Bell-CHSH inequality using entangled electron spins [link]
4 Sep, 10 Sep: Mixed state entanglement: PPT criterion.
Extra reading: Arul Lakshminarayan's article on Borromean triangles and the GHZ state .
Quantum Circuits and Algorithms
11 Sep: Classical computation: Circuit model, universal gates.
12 Sep: Complexity classes: P, NP and BPP
Extra reading: AMS feature article on PRIMES is in P [link]
18 Sep: Reversible computation and Landauer's principle
21 Sep: Quantum gates: Paulis rotations, controlled operations
25,28 Sep: Quantum Circuit Model: Gates, measurements, exact universality.