Benchmarking regularisation methods for quantum process tomography on NISQ devices

Abstract

Quantum process tomography (QPT) is a crucial tool for characterizing and validating quantum devices and quantum algorithms. However, the problem of finite sampling leads to an estimated process matrix which is non-positive semi-definite (non-PSD), which can yield a reconstructed quantum channel that is non-physical. To address this problem, various methods have been proposed to correct the issue of finite sampling in the estimation of the process matrix. In this work, we perform a comparison of regularisation methods that will be used to tackle the problem of finite sampling in QPT. For this comparison we simulate some common single qubit quantum channels. We use two metrics, the minimum eigenvalue of the Choi matrix and the fidelity, to compare the effectiveness of these methods. Our results show that the spectral transformations perform the best overall in dealing with finite sampling present in reconstructing the quantum channel in the NISQ era.