l l+2·r l+4·r l+6·r l+8·r l+10·r l+12·r l+14·r l+16·r l+18·r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Index Amplitude (a ) l = 3 r = 13 25 50 75 100 125 150 175 200 225 250 0.05 0.1 0.15 0.2 0.25 r 2·r 3·r 4·r 5·r 6·r 7·r 8·r 9·r 10·r 11·r 12·r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Index Amplitude (b) l = 0 r = 25 6 / 13 25 50 75 100 125 150 175 200 225 250 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Figure 1: An example of the operation of the QFT on a periodic state. The periodic state of q = 8 qubits with period r = 13 and shift l = 3 was transformed by the QFT. The amplitudes of the original state are given (a), as well as the amplitudes of the resulting state (b). The dotted vertical lines mark the multiplicands of the periods of each state ( Q/r ≈ 19 . 7 ). 20