Parameter estimation of quantum processes using convex optimization

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.

References in corpus (5)

• Quantum Process Tomography: Resource Analysis of Different Strategies
• Optimizing Completely Positive Maps using Semidefinite Programming
• Maximum-likelihood reconstruction of CP maps
• Optimal parameter estimation of depolarizing channel
• Optimal Experiment Design for Quantum State and Process Tomography and Hamiltonian Parameter Estimation

Cited by in corpus (1)

• Experiment design and parameter estimation of Pauli channels using convex optimization