I suggest you read the student manuals for GSoC.
Submit a proposal how you want to approach this project, including technical details (as much as possible) and detailed timelines.
Regarding the following:
1 First, understand how BooleanScorer calls these similarity classes and does the scoring. There are unit tests in Lucene that can help you get there. This might help: https:2 Write a standalone CUDA/OpenCL project that does the same processing on the GPU.
3 Benchmark the speed of doing so on GPU vs. speed observed when doing the same through the BooleanScorer. Preferably, on a large resultset. Include time for copying results and scores in and out of the device memory from/to the main memory.
4 Optimize step 2, if possible.
If you've already understood step 1, feel free to make a proposal on how you will use your GSoC coding time to achieve steps 2-4. Also, you can look at other stretch goals to be included in the coding time. I would consider that steps 2-4, if done properly and successfully, is itself a good GSoC contribution. And if these steps are done properly, then either Lucene integration can be proposed for the latter part of the coding phase (last 2-3 weeks, I'd think), or exploratory work on other part of Lucene (apart from the BooleanScorer, e.g. spatial search filtering etc.) could be taken up.
Time is running out, so kindly submit a proposal as soon as possible. You can submit a draft first, have one of us review it and then submit it as final after the review. If the deadline is too close, there might not be enough time for this round of review, and in such a case just submit the draft as final.
Also, remember a lot of the GPGPU coding is done on C, so familiarity/experience with that is a plus.
(Just a suggestion that makes sense to me, and feel free to ignore: bullet points work better than long paragraphs, even though the length of sentences can remain the same)