Declared dead by who?
The academic world? The Computing Science community? In the 80s and
the 90s, AI was defocussed on. It of course never disappeared, but it
certainly wasn't as prominent as in the late 70s and early 80s.
What were they referring to by AI?
Eh, "Artificial Intelligence"? ;-) Making complex decisions as fast
and in a similar way as humans can?
I just read through the paper you referred to, and it looks a bit
bullshit to me. P and NP problems are defined for Turing
machines, quantum machines are a fundamentally different class of
machines. There are other machines possible where it hardly makes
sense to talk about P and NP (take for instance an oracle and each
time your algorithm has to guess, you ask the oracle instead).
I do however have serious doubts about the feasability of quantum
computers. Perhaps when the NSA starts decrypting 4096 bit GPG
messages almost instantly I'll become a believer.