Can Quantum computing address the limitations of Classical computing

Yes, and the answer boils down to two fundamental quantum effects-

1. Superposition
2. Entanglement

Even before explaining these effects let us understand the limitations of classical computing. 

Classical computing works with binary, there are loads of bits which can be either be in a state of 0 or 1. And so, if we want to search through a whole load of different states, a classical computer has to search them one by one. Now this is time consuming and can render errors or even lead the system to crash.

This is where a quantum computer solves the issue with exponential scaling.