Possible mentor: Nuno Lopes
Make a tool to convert Zend bytecode into LLVM bitcode. Some work has already been done last year. A basic JIT engine already works. Features missing include: stabilization, code sharing between Apache/FastCGI processes, further optimizations, generate self-executable applications (without the PHP sources at all), etc.. (VMKit might be a good source for inspiration)
Code that does basic JITing works. It can run successfully most of the test suite already. Needs heavy refactoring for newer LLVM versions.