There is no classical algorithm for $n$-bit TQBF with better than $O(2^n)$ complexity. Is that also the best known bound for quantum algorithms / circuits?
Edit: As pointed out by Huck Bennett, in the full alternation subset of TQBF we can in fact beat $O(2^n)$ via randomized tree search. This is the case I care about most, so I would also be curious for the best exponent for a quantum algorithm if there are all $n-1$ quantifier flips.