1. Adiabatic Quantum Computation (AQC)
AQC, though formally equivalent to circuit model QC, is quite different in its formulation. What are the advantages, and disadvantages of AQC compared to the circuit model? What are some promising physical systems in which to implement AQC? There has been a lot of recent work analyzing the DWave quantum annealing machine, which is similar to an adiabatic quantum computer (but not the same). What is this machine, and what is the current understanding of how it works and whether it is a fully quantum system?
2. Quantum simulation
What is the difference between digital and analog simulation?
What the issues in both?
What are the physical systems that people propose to do quantum simulation with, and what system do they propose to simulate?
Cirac, J. I., & Zoller, P. (2012). Goals and opportunities in quantum simulation. Nature Physics, 8(4), 264–266. doi:10.1038/nphys2275
Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M. (2012). Can one trust quantum simulators? Rep. Prog. Phys., 75(8), 082401. doi:10.1088/0034-4885/75/8/082401
Tomi H Johnson, S. R. Clark, D. Jaksch. (2014). What is a quantum simulator?, EPJ Quantum Technology, 1, 10. doi:10.1140/epjqt10
3. Quantum computing technology (diamond, ion trap, linear optics, superconducting circuits, neutral atoms, …)
4. Foundations, interpretation of quantum mechanics. Especially the recent Pusey, Barrett, Rudolph result.
5. Algorithmic cooling
6. Quantum error correction
-Why is it necessary, what are the relevant thresholds, what's experimental progress in this direction?
7. Magic state distillation
-What is it, what is a simple protocol, what is the state of the art?
8. Topological quantum computation.
-What is it, how is it different from circuit model QC, what are candidate physical systems?
9. Quantum money
-What is it, how does it work, (could tie in to quantum encryption, communication etc.)
10. Boson Sampling and the possibility of quantum computation
-What is it, why is it interesting, could tie in to other criticisms of the possibility of quantum computation
11. Pick and discuss your favorite algorithm:
12. Other models of quantum computation
-One clean qubit (DQC1) - http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.5672
-Measurement-based quantum computation
-Quantum Turing machine
Quantum random walks
13. Discuss a particular quantum
simulation in detail
14. Bell-type experiments, and
closing various loopholes:
see also 10.1103/PhysRevLett.90.157904,
15. Weak measurements and weak values
and Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988),
but see also Ferrie and Combes, PRL 113, 120404 (2014)