Can current quantum computers decide languages that Turing Machines cannot?
No. A state of $n$ qubits can be represented with a vector of size $2^n$, and quantum gates can be implemented as linear operations for those vectors. Therefore a quantum computer can be simulated with a Turing machine, although with an exponential overhead. It is also known that the class of problems solvable by a quantum computer in polynomial time, BQP, is contained in the class of problems solvable by a classical computer in polynomial space, PSPACE.

All this information is from the Wikipedia page https://en.wikipedia.org/wiki/Quantum_computing