The final computational step, like the first, is again a purely quantum mechanical one. It is easy to see that this is reversible via the inverse transform and indeed it is readily verified to be unitary. Suppose has period r so . All other values of will produce destructive interference to a greater or lesser extent. 11 Plot of the probability of each result versus .
Constructive interference produces narrow peaks at multiples of the inverse period of the sequence .
One complete run of the quantum computer yields a random value of underneath one of the peaks in the probability of each result . That is, we obtain a random multiple of the inverse period. Thus, this algorithm yields only a probabilistic result. Fortunately, we can make this probability as high as we like. All the above work may appear a little anti-climactic.