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That's not what I'm saying. I'm saying that if factoring were NP hard, by extension a quantum computer could solve NP complete problems in polynomial time (sinc
by misterrobot 10y ago
That's not what I'm saying. I'm saying that if factoring were NP hard, by extension a quantum computer could solve NP complete problems in polynomial time (since every problem in NP is reducible to every NP hard problem, by definition [0]).
That's all I'm saying... they're implying that you could reduce, say, 3SAT to factoring, which would be very very surprising.
[0] https://en.wikipedia.org/wiki/NP-hardness https://en.wikipedia.org/wiki/NP-hardness
- dalke 10y agoI do not believe quantum computers can solve NP hard problems in polynomial time. According to https://en.wikipedia.org/wiki/BQP#Relationship_to_other_complexity_classes https://en.wikipedia.org/wiki/BQP#Relationship_to_other_comp... , "The relation between BQP and NP is not known." ("BQP (bounded error quantum polynomial time) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances.")
- rlanday 10y agoRight, it’s not known. Although technically we don’t know for sure if classical computers can solve NP-hard problems in polynomial time either (that’s the P vs. NP problem).