Equals DSPACE(22O(n)).
Is not contained in BQP/qpoly [NY03].
The class of problems solvable by a BQP machine that receives a quantum state ψn as advice, which depends only on the input length n.
As with BQP/mpoly, the acceptance probability does not need to be bounded away from 1/2 if the machine is given bad advice. (Thus, we are discussing the class that [NY03] call BQP/*Qpoly.) Indeed, such a condition would make quantum advice unusable, by a continuity argument.
Does not contain EESPACE [NY03].
[AD14] showed that BQP/qpoly = YQP/poly.
There exists an oracle relative to which BQP/qpoly does not contain NP [Aar04b].
A classical oracle separation between BQP/qpoly and BQP/mpoly is presently unknown, but there is a quantum oracle separation [AK06]. An unrelativized separation is too much to hope for, since it would imply that PP is not contained in P/poly.
Contains BQP/mpoly.
Does not contain PP unless CH collapses [Aar06],[Yir24].