Optimal depth and a novel approach to variational unitary quantum process tomography

Abstract

In this work, we present two new methods for variational quantum circuit (VQC) process tomography (PT) onto n qubits systems: unitary PT based on VQCs (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 PT and decreases the required state initializations from 4n to just 2n, 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 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. 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.