What is a Quantum Computer?

The New Scientist answers the question What is a Quantum Computer?

Classical computers, which include smartphones and laptops, encode information in binary "bits" that can either be 0s or 1s. In a quantum computer, the basic unit of memory is a quantum bit or qubit.

For instance, eight bits is enough for a classical computer to represent any number between 0 and 255. But eight qubits is enough for a quantum computer to represent every number between 0 and 255 at the same time. A few hundred entangled qubits would be enough to represent more numbers than there are atoms in the universe.

In situations where there are a large number of possible combinations, quantum computers can consider them simultaneously. Examples include trying to find the prime factors of a very large number or the best route between two places.

That last paragraph above exposes the problem for not just Bitcoin security but virtually all public-private key password encryption. 

How Can 7 Bits Represent So Much?

Technology review describes superposition.