Quantum computing is a generalization of classical computing. Thus, they CAN do classical computing. But, in practice, it'll be not as fast, more error prone and at a bigger cost.
Any basic operation you can do with reversible computing on bits, can be done with qubits.
Any basic operation you can do with normal computing on bits can be done with reversible computing on bits provided that you have enough ancillary bits to store the information that would normally be deleted in the irreversible normal operation on bits.
