Quantum computers are Boltzmann machines, operating at Monte Carlo method in hardware level.

http://en.wikipedia.org/wiki/Monte_Carlo_method

http://en.wikipedia.org/wiki/Boltzmann_machine

A compression algorithm composed of neural networks, with each cell performing statistical calculations, it would have an infinite speed, and would be using the full potential of the quantum computer - Combining PPM + CTW elements.

All quantum processors so far, using a few qubits, and the rest is conventional computing.

The consistency of data would be maintained by conventional part.