PH5610: Quantum Information and Many-Body Systems

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

Prerequisites: PH5007

Syllabus

Module 1: Measures of quantum correlations

( Lecture hours: 14 , Tutorial hours: 0 , Lab hours: 0 )

Qubits and Bloch sphere representation, projection measurement, density matrices, Pure and mixed states: definitions, examples, importance, Partial trace and partial transposition, Bloch representation of density matrices, Introduction to entanglement: Shannon and von Neumann entropy, Entanglement in pure states, Bell states, entanglement in mixed states, Other relevant measures, entanglement and interaction between qubits, other quantum correlation measures .

Module 2: Interacting quantum spin systems

( Lecture hours: 17 , Tutorial hours: 0 , Lab hours: 0 )

One-dimensional XY and Ising model in a transverse field, Jordan-Wigner (JW) transformation, determination of phase diagram, Magnetization and spin-correlation functions, One-dimensional XXZ model with/without magnetic field and failure of JW transformation, Nearest and next-nearest neighbor density matrices from symmetries of these models, Calculation of entanglement measures (example: concurrence), Spin chains at finite temperature .

Module 3: Applications of spin systems in quantum information

( Lecture hours: 11 , Tutorial hours: 0 , Lab hours: 0 )

Quantum state transmission, Cluster states, Measurement-based quantum computation .

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 Phase Transitions, S. Sachdev, Cambridge University Press (2011), ISBN: 978-0521514682

References

  1. Quantum Computing Explained, D. McMahon, Wiley-Interscience (2007), ISBN: 978-0-470-09699-4
  2. Quantum Information Theory, M. M. Wilde, Cambridge University Press (2013), ISBN: 978-1107034259
  3. 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:
  4. Quantum Physics in One Dimension, T. Giamarchi, Oxford Science Publications (2003), ISBN: 978-0-19-852500-4