Figure 1. Outline of quantum circuit for computing the square-free part for N = pq².

The procedure denoted as Ω in the text consists of two main parts. In the first part, we generate the state |φ〉; in the second part, we apply the quantum Fourier transform (QFT) to it. Single lines represent qubits, and boxes represent operations. Time runs from left to right. The transformation U₁ and U₂ are defined by Eq. (5) and Eq. (6). The meters M₁ and M₂ represent the measurements. The double lines coming from M₁ carry the classical bits, here the algorithm continues only if register B collapses to 1.