Sorry, there is no Advanced Grading (i.e. rubrics) available in the Quiz module.
But I recommend you take a look at the new Essay (auto-grade) question type plugin. It is the same as the standard Essay question type, but auto-grading has been added. Auto-grading immediately gives feedback and a score to the student based on: 1) word count/character count, 2) use of designated key words, or 3) both. Teachers must, of course, review the scoring and adjust it later for the quality of essay writing. But students do not have to wait for initial feedback. This contributed plugin made by Gordon Bateson, is available by searching the github code base here.
Quiz
Essay grading
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