Appendix A

Class Stuff

By now there seem to be quite a few books on quantum computing. However, I have only a few which I am recommending for the course. (These are in no particular order.)

• Visit http://www.qubit.org and click on “What is QIP?” There are several introductory articles there about quantum mechanics and quantum computing. There are other interesting articles as well.
• N. David Mermin’s book [11].

  Paraphrasing from the book: This book was written as an introduction to quantum computation which does not assume any background in physics. It evolved from his course on quantum computing for undergraduate and graduate students at Cornell and is for students from computer science, mathematics, engineering, and physics.

  I have heard him speak and read another book of his. His explanations are great.

• Shankar’s book: Principles of Quantum Mechanics

  The book contains topics which are more advanced, but starts fairly simply and the primary reason I list it here is that the first chapter has a lot of the mathematics that we will be using (and probably more) written at a fairly basic level, although it is somewhat abstract.

• Michael Nielsen and Isaac Chuang’s book [13].

  This book has a little bit about many different subjects. Its easy to read (for the most part) and contains very important and fairly basic information. This has been THE textbook and reference book since about 2001.

• John Preskill’s Course notes [9].

  Amazing! These notes were essentially THE textbook treatment before the book of Neilsen and Chuang book and are still very good for a variety of introductory topics as well as a good reference for a variety of topics. Some of them quite advanced. It’s available on the web!

• Frank Gaitan’s book [5].

  To my knowledge this is the first book on quantum error correction. Approximately the second half of the course will cover quantum error prevention methods.

Outline for the Course

1. Quantum Computation: Why? How? What does it mean?
2. Quantum Mechanics: Qubits
   • Some math stuff: matrix algebra, notation, and tensor products
   • Qubit States
   • Some Simple Gates - Qubit Gates
   • States of Many Qubits
   • Circuit Diagrams and some not-so-simple gates (an example of a two-qubit gate)
   • Measurements
3. Quantum Mechanics: The Physics Behind the Information
   • Some physics behind the information: ideas
   • Solving the Schr¨odinger equation: Formally, AKA Quantum gates
   • Density operators, open systems
   • Expectation values
   • Entangled States
   • Measures of Entanglement (Skip)
4. Uses of Quantum Information: Simple Examples
   • Uncertainty: the idea of incompatible observables
   • No-cloning!
   • BB84, Quantum Key Distribtion (QKD)
   • Dense Coding
   • Quantum Teleportation
5. Quantum Computation
   • Prerequisites
     1. Universal sets of Gates
     2. Useful constructs
   • Deutsch-Josza
   • Why factor? RSA encryption
   • Quantum Fourier Transform
   • Shor’s algorithm for factoring
   • Grover’s: We can search (among other things) more efficiently
6. Experiments: Physical Implementations (ideas/gates in brief)
   • NMR
   • Solid-State qubits
   • Ion Traps
   • Neutral Atom Traps
   • Photons for Quantum Information Processing
7. Noise in quantum systems: States, Effects, and Operations as well as Markovian vs.non-Markovian noise
   • Review of the density operator
   • States and operations on states
   • Noise and imperfect unitary operations
   • Modeling noise and understanding noise
   • Markovian noise and approximations
8. Quantum Error Correcting Codes
   • Basics and Examples
   • Stabilizer Codes
   • Threshold Theorem(s)
9. Decoherence-free/Noiseless Subsystems
   • More Group theory
   • Decoherence-free subspaces
   • Noiseless subsystems
   • Quantum Computing in a DFSs
10. Dynamical Decoupling Operations
    • A first-order theory: The bang-bang limit
    • Higher-order terms and other pulses
11. Combining Error Prevention Methods
    • Simple Examples
    • General Features/Theorems
    • More complicated examples
    • Tactics for Using Experimental Data

Grades

• There will be four homework assignments. Each will be given 10 to 14 days before the due date.
• There will be one class project. You will choose a research topic that interests you and write a short paper on it and present what you learned in class. You may collaborate on this project. However, each person must present their own work in class.
• There will be a web site which will have all of the class notes and more. However, the notes will not be posted before the lecture.
• The final grade will be given based on the homework and project, one part for each. (The weight is 20% for each assignment.)
• You are encouraged to write your paper so that it could be posted on the web site for everyone to read. (The web site will eventually be publicly available - after the end of the semester.) Your project may or may not be publishable in a journal. However, it will be publishable on the web site if it is well-written even if it is not new. This is your chance to publish an article.