In this work, we present two new methods for Variational Quantum Circuit (VQC) Process Tomography onto \(n\) qubits systems: unitary Process Tomography based on Variational Quantum Circuits (PT\_VQC) and Unitary evolution-based Variational Quantum Singular Value Decomposition (U-VQSVD). 

Compared to the state of the art, PT\_VQC halves in each run the required amount of qubits for unitary process tomography and decreases the required state initializations from \(4^{n}\) to just \(2^{n}\), all while ensuring high-fidelity reconstruction of the targeted unitary channel \(U\). It is worth noting that, for a fixed reconstruction accuracy, PT\_VQC achieves faster convergence per iteration step compared to Quantum Deep Neural Network (QDNN) and tensor network schemes.

The novel U-VQSVD algorithm utilizes variational singular value decomposition to extract eigenvectors (up to a global phase) and their associated eigenvalues from an unknown unitary representing a universal channel. We assess the performance of U-VQSVD by executing an attack on a non-unitary channel Quantum Physical Unclonable Function (QPUF). By using U-VQSVD we outperform an uninformed impersonation attack (using randomly generated input states) by a factor of 2 to 5, depending on the qubit dimension.

For the two presented methods, we propose a new approach to calculate the complexity of the displayed VQC, based on what we denote as optimal depth.