Introduction to quantum information processing (CO 481/CS 467/PHYS 467, Winter 2014): Course project

Guidelines

For the course project, you should write an expository paper on a topic of your choice from the quantum information literature. Your goal should be to understand a new concept in quantum information by reading original sources, and then to communicate this concept clearly and concisely. Your target audience should be your fellow students in the course.

Your paper should be at most ten pages in length (not counting references), using at least 11-point fonts and at least 1-inch margins. You are strongly encouraged to prepare your paper using LaTeX; you might use this template (illustrating a few basic commands) to get started. If necessary, you can draw quantum circuits using the Qcircuit package. Feel free to ask the instructor and the course TAs for help with typesetting in addition to your chosen topic.

You may find it helpful to read a sample paper from a previous year's class. This is an example of a paper that is well-written and presented at an appropriate level.

Deadlines

Please send email by February 27 to indicate your chosen topic. Your email should include a one-paragraph description of the material you plan to cover and a list of your primary references. I encourage you to discuss your choice of topic with me well before this date (especially if you would like to choose a topic that is not on the list). Each student should have a unique topic, and topics will be assigned on a first-come, first-served basis.
Papers should be submitted as a PDF file sent by email to amchilds@uwaterloo.ca. They are due by 11:59 pm on the date of the last lecture, April 3.

Topics

The following is a list of possible project topics, organized by subject, with a link to a reference for each. Though long, this list is far from exhaustive; you are welcome to choose a topic not on this list or to use a different paper as your primary reference.

Most of these references are links to published articles that may not be accessible from outside the university. Let me know if you have difficulty accessing any of these references. I have listed only one paper for each topic. In many cases, the choice of reference is somewhat arbitrary; you are encouraged to consult other related papers. Please do not hesitate to ask if you would like additional references for some topic.

Quantum circuits
Quantum algorithms
- Decomposing Abelian groups
- Algorithms for solvable groups
- Hidden shift problems
- Solving Pell’s equation (and other quantum algorithms for number fields)
- Query complexity of the nonabelian hidden subgroup problem
- Subexponential algorithm for the dihedral hidden subgroup problem
- Query algorithms for graph properties
- Matchings and network flows
- Discrete-time quantum walk on the line
- Exponential algorithmic speedup by quantum walk
- Quantum walk algorithm for element distinctness
- Quantum walk search algorithms
- Evaluating game trees
- Span programs
- Learning graphs
- Quantum rejection sampling
- Quantum oracle interrogation
- Searching an ordered list
- Quantum adiabatic optimization
- Approximating the Jones polynomial
- Hamiltonian simulation
- Linear equations
- Simulating quantum field theory
- Or find another quantum algorithm that interests you at the Quantum Algorithm Zoo
Lower bounds on quantum query complexity
Quantum computational complexity
Quantum error correction and fault tolerance
- Stabilzer codes (focus on chapters 2-4)
- The threshold theorem
- Decoherence-free subspaces
- Subsystem codes
Quantum cryptography
Quantum information theory
Alternative models of quantum computation
Implementations