Synthetic dataset D

The synthetic dataset D used in the main text is constructed by generating a set of data points {x(i)} with x(i) ∈ R3. The optimal circuit is Ux = RY(x1) ⊗ RY(x2) ⊗ RY(x3). The strategy to label x(i) is as follows. Let Π = I4 ⊗ |0(cid:105) (cid:104)0| be the measurement operator. The data point x(i) is labeled as y(i) = 1 if (cid:104)000|U †x(i)U ∗(θ∗)†ΠU ∗(θ∗)Ux(i) |000(cid:105) ≥ 0.75. The label of x(i) is assigned as y(i) = 0 if (cid:104)000|U †x(i)U ∗(θ∗)†ΠU ∗(θ∗)Ux(i) |000(cid:105) ≤ 0.25.