EE290: Special Topics in Control-Spring 2012

Introduction to Quantum Dynamics and Control

Time: M-W 10:30-12:00 PM

Location: 400 Cory Hall

EE290: Special Topics in Control-Spring 2012

Introduction to Quantum Dynamics and Control

Time: M-W 10:30-12:00 PM

Location: 400 Cory Hall

Course Description: This math-oriented course gives an introductory overview of quantum systems control theory for engineering students with interests in multi-disciplinary research or new control theory challenges.

Recent technological achievements have reached new horizons in manufacturing small-scale devices. The size of novel miniaturized objects necessitates a quantum mechanical treatment of their physical behavior. As in any other engineering paradigm, identification and control are essential ingredients of the design of quantum machines. During the last two decades, quantum control grown from a small specialty into a full-fledged field of research in science and engineering. This course is designed to introduce the essential developments in the theory of quantum systems control to graduate and senior undergraduate engineering students that have no background in quantum mechanics. It will also provide the basic knowledge required for pursuing research in this field.

Pre-requisites: Knowledge of linear algebra, differential equation and probability theory is assumed.

Background in control theory and quantum physics is desirable.

****** Homeworks *******

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Course Outline:

Quantum Dynamics:

Week 1- Quantum technology overview, (Slides)

Linear algebra for quantum mechanics (Notes)

Week 2- Quantum mechanics laws in nutshell (Notes)

Week 3- Physical examples: Quantum Bit, Harmonic Oscillator.

Week 4- Open quantum system dynamics: (Notes)

Quantum dynamical map (Kraus map representation)

Quantum dynamical equation (Master equation)

Open-loop control:

Week 5- Basic concepts and tools from geometric control theory:

Manifold, Lie algebra and Lie group, Controllability. (Notes)

Week 6- Coherent quantum control principles (Notes)

Week 7- Numerical optimal quantum control - Guest lecturer: Michael Goerz (Slides, Notes)

Week 8- Application to MRI: NMR Spectroscopy (Notes)

Week 9- Application to quantum computation: Quantum Gate

Closed-loop control:

Week 10- Basic concepts and tools from stochastic control theory:

Random process, Stochastic differential equation, Filtering problem (Notes)

Week 11- Continuous quantum measurement (Notes)

Week 12- Quantum feedback control principles (Notes)

Week 13- Application to NEMS: Feed cooling of a nano-mechanical resonator (Notes)

Week 14- Student project presentations

Course Evaluation:

Problem sets (50%), a project on a topic not covered during the course (40%) and class participation (10%).

The project will be delivered both as a written report and also in-class presentation.

This course is sponsored by Prof. Whaley, the director of the Berkeley Quantum Information and Computation Center.

Textbook and Reading List:

There is no required textbook. Main source of the course material are the following two books:

Domenico D'Alessandro, Introduction to Quantum Control and Dynamics, Chapman & Hall (2008).

Howard M. Wiseman (Author), Gerard J. Milburn, Quantum Measurement and Control, Cambridge University Press (2009).

Recommended Readings:

Linear Algebra:

- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2011).

- Gilbert Strang. Linear Algebra and Its Applications, Thomson Brooks/Cole (2006).

- Thomas F. Jordan, Linear operators for Quantum Mechanics, Dover Publications (2006).

Quantum Mechanics:

- David J. Griffiths, Introduction to Quantum Mechanics, Prentice Hall (1994).

- C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics , Wiley-Interscience (1978).

- Leslie E. Ballentine, Quantum mechanics: a modern development, World Scientific (1998).

- M. A. - Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2011).

- H-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2002).

- V. Braginsky and F. Khalili, Kip S. Thorne, Quantum Measurement, Cambridge University Press (1995).

Differential Geometry, Lie Algebra/Group Theory:

- Mikio Nakahara, Geometry, Topology and Physics, Taylor & Francis (2003).

- Ralph Abraham, Jerrold E. Marsden, Tudor S. Rațiu, Manifolds, Tensor Analysis, and Applications, Springer (1988).

- B. Hall, Lie Groups, Lie Algebras, and Representations, Springer-Verlag (2003).

Control Theory:

- S. Sastry, Nonlinear Systems: Analysis, Stability, and Control, Springer-Verlag (1999).

- Velimir Jurdjevic, Geometric control theory, Cambridge University Press (1997).

- P.R. Kumar and P. Varaiya, Stochastic Systems, Prentice-Hall (1986).

- Ramon van Handel, Stochastic Calculus, Filtering, and Stochastic Control, Lecture Notes, available at www.princeton.edu/~rvan/acm217/ACM217.pdf.

Probability and Stochastic Process:

- A. Papoulis, Probability, Random Variables and Stochastic Processes, Mcgraw-Hill College (1991).

- K. Jacobs, Stochastic Processes for Physicists: Understanding Noisy Systems,Cambridge University Press (2010).

- C. Gardiner and P. Zoller, Quantum Noise, Springer (2004).

- R. van Handel, Stochastic Calculus, Filtering, and Stochastic Control, Lecture Notes, available

at www.princeton.edu/~rvan/acm217/ACM217.pdf.