PH (complexity)

[1] It is a special case of hierarchy of bounded alternating Turing machine.

It even contains probabilistic classes such as BPP[2] (this is the Sipser–Lautemann theorem) and RP.

However, there is some evidence that BQP, the class of problems solvable in polynomial time by a quantum computer, is not contained in PH.

[5] This may simplify a potential proof of P ≠ NP, since it is only necessary to separate P from the more general class PH.

PH is a subset of P#P = PPP by Toda's theorem; the class of problems that are decidable by a polynomial time Turing machine with access to a #P or equivalently PP oracle), and also in PSPACE.