WebOct 31, 2024 · $\begingroup$ thanks. I understand. And in the case mentioned above (as of the knowledge we have now) we won't know anything more about the relationship b/w two sub branches below, even in the event of this collapse: namely NP, MA, AM and PSPACE and the other being the quantum ones BQP and QMA?
Consequences of BPP=BQP - Theoretical Computer Science Stack Exchange
WebOct 25, 2009 · The class AM is contained in the so-called polynomial hierarchy, while on the other hand, BQP, let alone QMA, is not believed to be contained in the polynomial … WebOct 22, 2024 · We should clarify that there are two questions here: whether B Q P ⊆ P H and whether P r o m i s e B Q P ⊆ P r o m i s e P H. In the unrelativized world, it is entirely possible that quantum computers can solve promise problems outside the polynomial hierarchy, but that all languages in B Q P are nevertheless in P H. michael vick live
BQP and the Polynomial Hierarchy - scottaaronson.com
WebFeb 2, 2024 · Thus, (it is believed that) BQP-complete problems cannot be solved in polynomial time on a classical computer. The hierarchy and relations of complexity classes relevant for this work are... WebThe relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence… Highly Cited 1999 Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses Adam R. Klivans, D. Melkebeek Symposium on the Theory of Computing 1999 Corpus ID: 7574830 In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP. Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines. It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarc… michael vick in prison