MA591: Mathematical Foundations of Quantum Computation

This is a special topic course that introduces you to the basic notions of quantum computation.

• Quantum technologies are pushing forward the frontiers of the future. As such, students should be curious and find it both beneficial and of vital importance that they are exposed to this subject as early as possible.
• Quantum computation is fundamentally different from the classical numerical analysis. Most of the topics covered in conventional computation will have to be reinvented, if possible at all, and many of which remain to be further researched.
• However, a solid grasp and holistic treatment of this subject will require disciplines across multiple academic fields, which is hard to come by. This course intends to serve only as a stepping stone by introducing this subject from the mathematical perspective.
• Mathematical and computational foundations useful for deciphering the rich structure within a quantum system and the quantum computation will be discussed.

Reading materials:

• My own lecture notes with materials from various resources for this course are available on line.
• The following books are the classical references for this subject in its entirety, but is probably deeper and broader:
1. Quantum Computation and Quantum Information, Nielsen and Chuang, Cambridge, 10^th Anniversary Edition.
2. Quantum Computing: from Linear Algebra to Physical Realizations, Nakahara and Ohmi, CRC Press, 2008.

Some useful tools:

• Unix Reference Desk
• Netlib: Numerical Analysis Library Network (Lots of library routines)
• AMS: American Mathematical Society (Math Review on line)
• NCSU Library: Enter it with an awesome heart and a humble attitude; out of it with a learned mind.
• Encyclopedia s and Dictionaries: Who says a mathematician doesn't need these?
• RBC: Something good for your souls
  

Grading Policy:

• final grade= (60% homework) + (40% projects)
• Homework is to be completed by individuals.
1. Homework will be assigned intermittently.
2. Homework is meant to fill in gaps of lectures. Do expect a fast turn-around when the homework is assigned.
3. Homework differs from projects in that

1. Homework is meant to fill in gaps of lectures. It usually involves some simple fact-checking mathematics. Do expect a fast turn-around when the homework is assigned.

2. Projects usually require some deeper research and preparation, such as reading relevant papers.

• Projects may be worked on and turned in by study groups of up to 2 people per group.
1. All group members receive the same grade.
2. Projects are related to skills learned in class, but most topics require additional endeavors to investigate new territories.
3. Project papers require specific format. All reports and figures must be computer generated.