Figure 1.

(a) The general framework of our VQPT method. By training the PQC with the quantum states in the training set $\Psi$ and validation set $\Phi$ and optimizing the parameters in $\mathcal{C}\left(\overrightarrow{\theta }\right)$ based on a gradient-descent approach, the PQC $\mathcal{C}\left(\overrightarrow{\theta }\right)$ gradually approximates the physical quantum process $\mathcal{O}$. (b) The structure of the PQC. It begins and ends with a single-qubit layer. Each two-qubit layer is counted as a depth, and the circuit contains d depths of operations and ends with a single-qubit layer.