Rather it performs a series of elementary operations whose net effect is to produce the new state vector . Let P be such a program. Then for each classical state s , i.e., a string of bit values, it produces an output , and each output is produced by only a single input. When used with a quantum superposition, such classical programs operate independently and simultaneously on each component to give a new superposition. This quantum parallelism allows a machine with n bits to operate simultaneously with different classical states.
Unitary operations can also mix the amplitudes in a state vector.
Since amplitudes are complex numbers, such mixing can combine amplitudes to leave no amplitude in some of the states.