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The best classical algorithm is not known to unconditionally run in [[polynomial time]]. The corresponding feasibility problem is known to either lie outside of the union of the complexity classes NP and co-NP, or in the intersection of NP and co-NP.<ref>{{Cite journal|url=https://doi.org/10.1007/BF02614433|doi = 10.1007/BF02614433|title = An exact duality theory for semidefinite programming and its complexity implications|year = 1997|last1 = Ramana|first1 = Motakuri V.|journal = Mathematical Programming|volume = 77|pages = 129–162|s2cid = 12886462|url-access = subscription}}</ref>
===The quantum algorithm===
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