What Are Advanced Dissertation Topics in Quantum Computing?

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FraserAC
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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 :)
 
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Do you prefer theoretical or experimental aspect of quantum computation? Are you more interested in the physics or the computer science side?
 
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.
 
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. :)
 
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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!