It is unknown whether quantum computing makes NP-complete problems easier to solve. There is a complexity class for problems that can be solved "efficiently" on using quantum computing, called BQP. How BQP and NP are related is unknown. In particular, if an NP-complete problem was shown to be solvable efficiently with Quantum Computing (and thus in BQP), this open (and hard) research question would be solved (or at least half of it).

Note that BQP is not "efficient" in a real-word fashion, but for theoretical study of Quantum computing, it's a good first guess

AFAIK, which is not much, I believe it is problems that you can turn in to a cycle. Right now we pull out answers from quantum computers at random, but typically do not know what the inputs were that got that answer. But if you can get the answers from the quantum computer to be cyclical you can use that symmetry to get all the information you need.