Optimal depth and a novel approach to variational quantum process tomography

TL;DR

This paper introduces two innovative methods, PT_VQC and U-VQSVD, for efficient quantum process tomography on n-qubit systems, reducing resource requirements and improving accuracy and speed over existing techniques.

Contribution

The paper presents two novel methods for variational quantum process tomography that significantly reduce qubit and initialization requirements and enhance convergence speed and accuracy.

Findings

PT_VQC halves qubit requirements compared to previous methods.

U-VQSVD effectively extracts eigenvectors and eigenvalues from unknown channels.

U-VQSVD outperforms random attack strategies by a factor of 2 to 5.

Abstract

In this work, we present two new methods for Variational Quantum Circuit (VQC) Process Tomography onto $n$ qubits systems: PT_VQC and U-VQSVD. Compared to the state of the art, PT_VQC halves in each run the required amount of qubits for 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 general channel. We assess the performance of U-VQSVD by executing an attack on a non-unitary channel Quantum Physical Unclonable Function (QPUF). U-VQSVD outperforms 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.