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A Dissertation Topic Ideas

  1. Sep 4, 2016 #1
    Hi! I'm going on to the masters year of a theoretical physics course and I need some inspiration for my dissertation. Last year I did a one semester long project on quantum computation. (More specifically I discussed the general idea of a qubit, a simple method of realising a qubit using spin and a simple example of a Quantum Fourier Transform algorithm). This year I'm doing a year long project that is supposed to continue on this theme and I'd love some suggestions on ideas I could discuss/study and some sources that would help me do so.

    Last year I mainly used Nielson and Chuang's Quantum Computing and Quantum Information textbook as a source, ideally I'd like multiple sources this year. My target this year is about twenty thousand words, so I'd need a topic (or multiple connected topics) that I could go into sufficient detail on.

    Thanks very much :)
     
  2. jcsd
  3. Sep 4, 2016 #2
    Do you prefer theoretical or experimental aspect of quantum computation? Are you more interested in the physics or the computer science side?
     
  4. Sep 4, 2016 #3
    Well, I enjoy the abstract theoretical nature of the maths, but also like attempting to connect it to something physical (I.e. in the project last semester I discussed spin of electrons and how to manipulate it physically using a set up similar to the Stern-Gerlach apparatus, as well as calculating the Hamiltonian needed for chosen change of state around the bloch sphere). However, I won't be performing any physical experiments.

    I'd say I'm more interested in the Physics, but I'd like to include at least a little computer science. My supervisor suggested attempting to program a simple quantum algorithm into the IBM quantum experience thing. I have no idea how to do that yet though, so that's a low priority.

    I hope that's not too vague. If it is I'd be happy to be more specific.
     
  5. Sep 5, 2016 #4
    From the top of my head:
    - More quantum algorithms: hidden subgroup algorithms (also using Fourier transforms) Grover's search algorithm, quantum walk, linear equation solver etc.
    http://www.nature.com/articles/npjqi201523
    - Complexity of simulating Hamiltonians, classical simulation using matrix product states, area laws of entanglement
    https://arxiv.org/abs/0808.3773
    https://arxiv.org/abs/1106.5875
    https://arxiv.org/abs/1603.03039
    - Non-universal quantum computation that is nevertheless provable (assuming P ≠ NP and its variants) to be hard for classical computers to simulate: linear optics with multi-photon input
    https://arxiv.org/abs/1406.6767
    - Quantum computation that is easy to simulated classically: stabilizer circuits, matchgate circuits
    http://arxiv.org/abs/1512.07892
    http://arxiv.org/abs/1602.03539
    - Decoherence, quantum error corrections and fault tolerance
    Daniel Gottesman's thesis and video lectures are good starting points
    https://arxiv.org/abs/1302.3428
    - John Preskill's lecture note is also a good general resource
    http://www.theory.caltech.edu/people/preskill/ph229/

    I hope this helps. I will be interested to hear which topic you settle on. :)
     
  6. Sep 6, 2016 #5
    Thanks very much! The quantum algorithms one sounds good and so does the Decoherence and quantum error corrections. I'll have a look over the next few days and make a final decision, then post it back on here. Very helpful though, thank you!
     
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