A final answer requires 2L calculations. With a quantum operator, L bits can be input once, and one calculation could contain all 2L possible numbers. This exponential speed-up is called quantum parallelism and is the chief attraction of quantum computation. This exponential leverage of resources is not without a down side, however. The superposition state is not completely accessible.
Any calculation is a rotation in the vector space.
This creates a new vector, and quantum mechanics does not allow the measurement of all output vectors. Quantum mechanics requires a collapse of the wave function from a superposition for measurement to occur, Kimble notes. This might seem a fatal constraint. Of the 2L pieces of information contained in the system, only L can be extracted. For example, returning to the electrons, each bit's spin can be measured, either up or down, providing L pieces of information.