### Project Examples

Several outstanding student projects are featured on Scott Aaronson’s blog.

### Project Description

All students taking 6.845 for credit are expected to complete a course project by the end of the semester.

The project can be either a survey of some topic in the quantum complexity theory literature, or original research. Projects can be done either individually or in groups of two. Pick a project that interests you, that’s at least somewhat related to the course, and that (crucially!) you’ll actually be able to finish by the end of the semester. Here are a few good ways to pick a project:

- Something mentioned in the course that you’d like to understand better
- Something not mentioned in the course that you wish had been
- Something that combines your own research interests with quantum complexity theory
- scholar.google.com, arxiv.org/find/quant-ph
- The last fifteen years’ proceedings of ACM Symposium on Theory of Computing (STOC), IEEE Foundations of Computer Science (FOCS), and IEEE Conference on Computational Complexity (CCC), as well as the list of talks at the annual Quantum Information Processing (QIP) conference

To help get you started, there’s a list of topic suggestions at the end of this section. Scott will also be happy to help you with additional suggestions and pointers to the literature. Here is what’s expected of you:

- Project Proposal. Submit a single paragraph describing your proposed project, together with a list of relevant papers. Please indicate if you are collaborating with anyone. Scott will then give you feedback and suggest additional relevant papers.
- Class Presentation. Each project group must give a 10-minute presentation during the final week of class. You can use blackboard or PowerPoint.
- Written Report. You must turn in a written project report by Lecture 26. The report should be up to five pages long, together with optional appendices that can be as long as you like and will be read at Scott’s discretion. (No, there are no rules about font size, margins, etc.; just be reasonable!)

#### Actual Projects from Last Iteration of the Course

- A QMA(k) protocol for 3SAT requiring unentangled measurements only
- Quantum Hidden Markov Models
- Simple presentation of the Solovay-Kitaev Theorem
- Universality of measurement-based quantum computing
- Lower bounds on quantum communication complexity
- Stoquastic Hamiltonians (Terhal, Bravyi, et al.)
- Quantum finite automata
- Classical simulation of quantum circuits
- Query-limited reducibilities and quantum computing

#### (Extremely Incomplete) List of Possible Other Topics

- Quantum cellular automata; equivalence with quantum circuits and quantum Turing machines
- Parallel implementation of Shor’s algorithm (Cleve and Watrous)
- Quantum Statistical Zero-Knowledge
- QIP = QIP (3) = PSPACE
- Quantum query complexity of compositions of Boolean functions (Reichardt)
- Quantum query complexity of graph-theoretic problems
- Quantum walk algorithms (Ambainis, Childs-Goldstone…)
- Real vs. complex numbers in quantum complexity theory
- Valiant’s matchgate theorem
- QMA-complete problems
- Complexity issues related to the quantum adiabatic algorithm
- Multi-prover quantum interactive proof systems: parallel repetition, etc.
- Continuous-time quantum query complexity
- Two-way quantum communication complexity (e.g., Razborov’s lower bound for Disjointness)
- One-way quantum communication complexity (e.g., )
- Quantum streaming complexity (Le Gall)
- Quantum Lovasz Local Lemma