PH5606: Quantum Information and Computation

L-T-P-C: 3-0-0-3

Prerequisites: PH5007

Syllabus

Module 1: Revisiting quantum mechanics

( Lecture hours: 12 , Tutorial hours: 0 , Lab hours: 0 )

Linear algebra: linear independence and bases, Hilbert space, tensor product, Postulates of quantum mechanics: state space, Hamiltonian, evolution, quantum measurement (projection measurement, POVM, generalized measurement), Density matrices for quantum states: pure and mixed states, Introducing qubits: two-level systems, Bloch sphere, Composite systems: partial trace and reduced states, Schmidt decomposition, EPR paradox and Bell inequality, entanglement .

Module 2: Quantum communication and cryptography

( Lecture hours: 12 , Tutorial hours: 0 , Lab hours: 0 )

No-cloning theorem, quantum teleportation, quantum dense coding, Quantum cryptography: BB84 and Ekert protocols, Multiparty scenario of quantum communication, Quantum state discrimination .

Module 3: Entropy and entanglement

( Lecture hours: 10 , Tutorial hours: 0 , Lab hours: 0 )

Basics of probability theory, Shannon entropy, von Neumann entropy, Conditional entropy and mutual information, Entanglement for pure and mixed states, Entanglement measures, entanglement witness, entanglement in multipartite systems .

Module 4: Quantum computation

( Lecture hours: 8 , Tutorial hours: 0 , Lab hours: 0 )

Introducing quantum algorithms (at least two examples), Quantum gates and quantum circuit elements, Introduction to quantum error correction (example of three-qubit bit-flip code) .

Study Materials

Textbooks

  1. Quantum Computation and Quantum Information, M. A. Nielsen and I. L. Chuang, Cambridge University Press (2007), ISBN: 978-81-7596-092-3
  2. Quantum Information Theory, M. M. Wilde, Cambridge University Press (2013), ISBN: 978-1107034259

References

  1. Lecture notes by John Preskill (ph229, ph219), John Preskill, http://www.theory.caltech.edu/people/preskill/ph229/ ; http://www.theory.caltech.edu/~preskill/ph219/ph219_2013-14, ISBN:
  2. Quantum Computing Explained, D. McMahon, Wiley-Interscience (2007), ISBN: 978-0-470-09699-4
  3. Introduction to Quantum Information Science, Vlatko Vedral, Oxford University Press (2013), ISBN: 978-0199673483