Classical computing relies on binary bits (0s and 1s) to process and store information, following well-defined algorithms that execute sequentially. Quantum computing, however, uses quantum bits or qubits, which can exist in superposition (both 0 and 1 simultaneously) and entanglement (where the state of one qubit is dependent on the state of another), allowing quantum computers to perform complex computations in parallel.

Quantum computing has the potential to revolutionize fields like cryptography and material science:

1. **Cryptography**: Quantum computers could break many of the widely-used cryptographic algorithms (such as RSA and ECC) due to their ability to perform calculations exponentially faster than classical computers using Shor’s algorithm. This could render current data encryption methods obsolete, prompting the need for new quantum-resistant cryptographic algorithms.

2. **Material Science**: Quantum computers can simulate quantum systems accurately, which is challenging for classical computers due to the computational resources required. This capability could lead to discoveries of new materials with specific properties, revolutionizing fields like drug discovery, energy storage, and materials design.

In summary, while classical computing operates linearly with binary bits, quantum computing leverages quantum mechanics to potentially solve complex problems exponentially faster. This difference could profoundly impact fields reliant on computational power, particularly cryptography and material science, by enabling faster calculations and simulations beyond the capabilities of classical computers.