Instructor

Navin Khaneja

Semester

Autumn’21

Course Difficulty

Moderate (with background), Difficult if this is your first course involving Lie Algebra

Time Commitment Required

1-4 hours per week for self-study (beyond lectures) depending on background. Prof’s notes are not self-sufficient and need to be supplemented by extra reading.

Grading Policy and Statistics

Standard grading on the curve, statistics can be found on asc (The class strength is usually quite small and quizzes/exams are on the easier side so relative grading becomes competitive)

Attendance Policy

There was no attendance policy. In online mode, recorded lectures were uploaded for reference. Prof Khaneja does not enforce attendance policies in offline mode as well.

Pre-requisites

Officially no prerequisites are mentioned. However, a basic understanding of quantum mechanics (at the level of QM1, not just PH107) is necessary to appreciate the later part of the course. NMR and spin systems are touched upon briefly and don’t need any serious pre-requisite knowledge.
As this is primarily a course on the intersection of physics & control, many basics are glanced over and a first course in control theory would be quite helpful.

Evaluation Scheme

Homework - 1 assignment per chapter - 4 chapters in total - 35%
Midsem - 25%
Endsem - 40%

Topics Covered in the Course

Chapter 1: Linear Systems - Basic differential geometry, vector fields, Lie groups, Lie algebras, Lie brackets.
Chapter 2: Non-Linear Systems - Theorem of Frobenius and Chow, nonlinear controllability.
Chapter 3: Optimal Control - Control systems on Lie groups, maximum principle and optimal control.
Chapter 4: Quantum Control - Fundamentals of spin dynamics and NMR. Coupled spin dynamics, time optimal control in NMR. Models of relaxation and decoherence in NMR, master equations and optimal steering. Ensemble control, broadband excitation and control, decoupling and recoupling. (Physics was kept quite basic while focusing on looking at the systems through control systems-perspective)

Teaching Style

The notes for all 4 chapters are provided on the Prof’s website, you can check them out. They are the primary reference. He uses slides/blackboard to teach with the same. Lectures are a bit difficult to follow but the material is quite interesting and the pace is easy to keep up with.

Tutorials/Assignments/Projects

The Assignments are provided at the end of the notes from day 1, and we were given plenty of time to solve them. Apart from a few typos and ill-defined questions, they were on the easy to medium side.

Feedback on Exams

No quizzes.
Midsem/Endsem: The exams were quite easy, including open notes and were usually completed well before time by everyone. If you have solved all the assignments, the exams were straightforward.

Motivation for taking this course

I am interested in control theory, quantum systems and this is relevant for both.

Course Highlights

The prof is extremely knowledgeable and has a great intuition for the subject. The notes are easy to follow and exams were easy, with the focus on understanding via assignments.

Course Importance

Useful to get a flavor of control theory in the context of physics for non-physics students. Also useful for physics students to understand applications of control theory to physics.

How strongly would I recommend this course?

Very strongly for those looking to get a taste of a different application of control theory.

When to take this course?

I took the course in my 9th semester (dropped it before endsem due to placements/PhD applications). I would recommend taking it in 3rd or 4th year after doing a basic course that covers Group Theory/Control Systems and QM1. You can take it alongside basic control systems course in 2nd year but understanding the quantum mechanics would become challenging.

Going Forward

Almost all electives by Prof Khaneja have significant overlap with one another and I would recommend all of those courses (in any order) alongside this course. I personally took SC638 (4th year) and SC641 (3rd year).

References Used

The Prof suggested the following:
1) V. Jurdjevic, “Geometric control theory”, Cambridge Univ. Press, 1997
2) J. Cavanagh, W. Fairbrother, A. Palmer, N. Skelton, “Protein NMR Spectroscopy”,
Academic Press, 2007
3) M. Goldman, “Quantum description of high resolution NMR in liquids”, Oxford
Univ. Press, 1988

I personally found it easier to use his notes and google the specific words/theorems I did not understand rather than use these books as the language and context were quite different.

Other Remarks

The workload for the course is on the easier side and I would recommend it for an institute elective.

Interesting relevant links

The entire field of Quantum Control builds from here. Optimally controlling quantum systems is one of the key challenges of quantum technology and this course gives a introductory flavor for the same.

Review By: Ajinkya Werulkar