Several programs can be used for the purpose of importing .pdf files with music sheets and saving it to a music sheet (like .mxl file), or in some cases directly to MIDI format, which is what pdf to midi conversion typically represents. This only works with PDF files that actually contain music data, usually exports from music writing programs.
A viable alternative to this would be to use some Musical OCR (OMR) solutions that can be used for recovery of music sheets from pictures and PDF files.Open PDF file Open MIDI file
A PDF sheet to music converter
A music scanning and notation program