Figure 3.

Quantum Circuit to compute ${\left|⟨,u,|,v,⟩\right|}^2$. The model circuits encode train and test data into quantum states $\left|u⟩=U,\left|q_1,q_2,q_3,⟩\right)\right)$ and $\left|v⟩=V,\left|q_4,q_5,q_6,⟩\right)\right)$. The Hadamard gate on the ancilla qubit ($q_0$) generates a superposition of the quantum state including the train and test datasets. The application of the single-controlled swap gates with the ancilla qubit as the control results in an entangled state of Eq. (10). Another Hadamard gate on the ancilla qubit interferences $\left|u⟩,\left|v,⟩\right)\right)$ and $\left|v⟩,\left|u,⟩\right)\right)$. The ancilla qubit on the $\left|0,⟩\right)$ state is measured in the Z basis. Therefore, the value of ${\left|⟨,u,|,v,⟩\right|}^2$ can be obtained from Eq. (12).