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.

Abigail