Algorithm 5 Conjugate Pair Oracle Fourier Sampling

Conjugate pair oracle:  $\mathcal{F}$ Control: none Bias/Target: conjugate pair $\mathcal{X}$ 1:create ancilla $\mathcal{Y}:=[y,\upsilon ]$ of length 1 with $\upsilon :=1$ 2:apply $\mathcal{F}$ to $(\mathcal{X},\mathcal{Y})$ 3:discard ancilla  $\mathcal{Y}$