While a conventional computer with N bits at any given moment must be in one of its 2^N possible states, the state of a quantum computer with N qubits is described by the values of the 2^N quantum amplitudes, which are continuous parameters (ones that can take on any value, not just a 0 or a 1). This is the origin of the supposed power of the quantum computer, but it is also the reason for its great fragility and vulnerability.

How is information processed in such a machine? That's done by applying certain kinds of transformations—dubbed “quantum gates"—that change these parameters in a precise and controlled manner.

Experts estimate that the number of qubits needed for a useful quantum computer, one that could compete with your laptop in solving certain kinds of interesting problems, is between 1,000 and 100,000. So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be at least 21,000, which is to say about 10^300. That's a very big number indeed. How big? It is much, much greater than the number of subatomic particles in the observable universe.

To repeat: A useful quantum computer needs to process a set of continuous parameters that is larger than the number of subatomic particles in the observable universe.