Quantum analogues of SPACE complexity classes
You might want to check  Space-Bounded Quantum Complexity, by John Watrous.

There you have the result that for any $s=\Omega(\log n)$, a Quantum Turing Machine running in space $s$ can be simulated by a probabilistic Turing Machine with unbounded error running in space $O(s)$. You also have that any Quantum Turing Machine running in space $s$ can be simulated in $NC^2(2^s) \subseteq DSPACE(s^2) \cap DTIME(2^{O(s)})$