Parameter estimation of quantum processes using convex optimization

TL;DR

This paper introduces a convex optimization approach for quantum process tomography that enhances parameter estimation accuracy when the channel model structure is known, especially for Pauli channels where it becomes fully convex.

Contribution

It proposes a semidefinite programming method for quantum channel parameter estimation leveraging convex relations, improving accuracy over existing methods.

Findings

Significantly increased estimation accuracy with known channel structure.

The method reduces to a convex problem for Pauli channels, ensuring global optimality.

Simulation results demonstrate the effectiveness of the approach.

Abstract

A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of optimization variables, and formulate a semidefinite programming problem with a least squares objective function. Possible convex relations between the optimization variables are also taken into account to improve the estimation. Simulation case studies show, that the proposed method can significantly increase the accuracy of the parameter estimation, if the channel model structure is known. Beside the convex part, the determination of the channel parameters from the optimization variables is a nonconvex step in general. In the case of Pauli channels however, the method reduces to a purely convex optimization problem, allowing to obtain a globally optimal solution.