QC's hype cycle

QC's hype cycle

The thing that could kill the QC hype cycle early is if quantum complexity theory can determine the relationship between BQP and NP.

The reason there's room for the sleight of hand merchants to hype QC is that we don't know how NP and BQP relate; the best we can do is to say that there are some problems (such as integer factorization) in both NP and BQP, that all problems in P are in both NP and BQP, and that we believe that some NP problems (like travelling salesman) are in NP but not BQP. But the hype merchants can argue that until Shor's algorithm was discovered, integer factorization was in NP only, and that there might be similar algorithms for a NP-complete problem.