Will we be able to solve all NP problems in polynomial time by 2200? (any practical computation method, e.g. BPP, BQP)

Question

Resolves YES if by 2200 humanity has the demonstrated capability to solve all NP problems in worst-case polynomial time, with error probability bounded by a constant. Otherwise resolves NO.

If you know about complexity classes: this means P = NP is sufficient but not necessary. BPP = NP (randomized algorithms with constant error probability) would be sufficient, and BQP = NP (quantum algorithms) would also be sufficient if the relevant algorithms could actually be run practically on quantum computers. Other methods could also be sufficient if they meet the resolution criteria.

Any method of computation is allowed for this question, as long as humans can actually do it practically and at reasonable scale. As an example: quantum computers can solve factorization (which is easier than NP-hard) in polytime, but I don't count factorization as solvable in polynomial time today because quantum computers can only do it on toy demonstrations currently.

Because this criteria may be somewhat subjective, the resolution will be based on expert consensus.

Manifold Markets · Answer

Almost certainly not — Manifold Markets prediction market estimates a 2% chance (15 traders, as of Jan 11, 2025).