Lie groups in quantum information

UNM Physics and Astronomy, Summer 2019 course (PHYC 500.001 Adv Sem)

The course materials are now hosted in a new site: http://info.phys.unm.edu/~pablo/summer2019.htm

Course coordinators:

General course information

This course is a survey of Lie groups and their applications to physics and quantum information. The course is designed to be a ‘self-study’ program. In the first two sessions, the course coordinators will give introductory lectures on Lie groups and Lie algebras. Reading material will be assigned every week, including lecture notes and research articles. In the remaining sessions, course participants will present sections from the reading material and facilitate group discussions. Participants are encouraged to also propose other topics of their interest.

Schedule

  • Session 1: [June 5th] Chris Jackson - Groups and symmetry [video]
  • Session 2: [June 12th] Chris Jackson - Lie algebras and analyticity [videos]
  • Session 3: [June 26th] Andrew Zhao - Semidirect products and normality [notes] [video]
  • Session 4: [July 3rd] Austin Daniel - Global classification of semisimple Lie groups [notes] [video]
  • Session 5: [July 10th] Anupam Mitra - Quantum Control [see bibliography below] [video]
  • Session 6: [July 17th] Gopi Muraleedharan - KAK decompositions [video]
  • Session 7: [July 24th] Tyler Thurtell - Non-compact semisimple Lie groups [notes] [video]
  • Session 8: [July 30th] Karthik Chinni - Representation theory I
  • Session 9: [July 31st] Manuel Muñoz - Representation theory II

Syllabus and bibliography

Click here to download the updated syllabus and bibliography for the course

Materials and exercises

Session 1

Session 2

Session 5 (Quantum control and Lie groups)

Some bibliography

  • V. Jurdevic and H. Sussman, Control systems on Lie Groups (link)
  • D. D'Alessandro. Introduction to Quantum Control and Dynamics (google books)
  • S. G. Schirmer, J. V. Leahy, A. I. Solomon, Degrees of controllability for quantum systems and applications to atomic systems (arxiv)