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fjelljenta / Quantum-Challenge

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Questions #4

Open mvanwaveren opened 1 year ago

mvanwaveren commented 1 year ago

Hello,

Thank you very much for publishing this repository. It is a nice example of the usage of quantum computing in the calculation of flight trajectories.

You write that you are convinced that the QUBO algorithm "is the most promising because with a careful design of mapping the available data onto a cost grid, and by cutting the cost grid into fine-enough voxels, one can perfectly recover the original continuous optimization problem for a single flight, just as the GA does it."

Does this mean the other quantum solutions, the QGA and the QNN, will not recover the original continuous optimization problem for a single flight?

I have some questions:

Regards, Matthijs van Waveren QC Expert at CS GROUP

kevinkayyy commented 1 year ago

Hello Matthijs,

We cannot say that QGA and QNN will for sure not recover the original continuous optimization. It is not trivial to tell which quantum algorithm will perform the best for this specific problem with a theoretical analysis. It's better to experiment and let the data speak. The QUBO method is interesting because it is well studied in the community and we know that by tuning the size of the voxels, we can approximate any curve in the space with arbitrary precision. There was only a quantum-inspired algorithm under the name of QGA by the time this project was done as far as I remember. Its expressiveness should be at least as good as GA, but the trainability and resources required needs further examination. The difficulty with QNN for this problem are how you parameterize the trajectory and map those parameters to the parameters of the QNN, and how you design the Ansatz. Also, we estimate that the QNN approach for this problem will pose high hardware requirements.

For the second question, I don't remember these details now, but you may check the challenge description: https://ekipa.cdn.prismic.io/ekipa/99f6f176-8f32-4be0-9a21-bed243c91487_DeloitteQuantumClimateChallenge2022.pdf

For the last question, I believe it is Kelvin per kilogram. You can confirm that in the challenge description as well.

Cheers, Kevin

mvanwaveren commented 1 year ago

Hi Kevin,

Thanks for your reply! I checked the document you mention, and I see now that the atmospheric data correspond to the climate effect delta C. The unit of the delta C is "K per kilogram fuel".

I made a fork of your repository, and I am modifying it. I will update the unit in the notebook. I also found an error that I fixed. I will open a pull request sometime in the future so you can see my modifications.

Cheers, Matthijs