Game of Numbers

 Clearly, the results of the Phase Estimation procedure are dictated by the play

of numbers under different constraints.

Fro theta at .9:

                                                                   

For theta at .3:

                                                                                

If I ask for theta at .75, I get:

*     *     *

Applying the transformation twice ups the frequency:

Twice and with another qubit:

The general Phase Estimation procedure uses as many qubits and repeats as necessary

for the precision required. With an eye to computational costs...