Confidence polytopes for quantum process tomography

TL;DR

This paper extends confidence polytopes from quantum state tomography to quantum process tomography, enabling reliable confidence regions for quantum channels using linear programming and demonstrating effectiveness with simulations and IBM quantum data.

Contribution

It introduces a generalized confidence polytope method for quantum process tomography, allowing for confidence regions of Choi matrices based on measurement data.

Findings

Effective confidence regions for quantum channels demonstrated.

Method scales well with system size and data complexity.

Validated with both simulated and real quantum processor data.

Abstract

In the present work, we propose a generalization of the confidence polytopes approach for quantum state tomography (QST) to the case of quantum process tomography (QPT). Our approach allows obtaining a confidence region in the polytope form for a Choi matrix of an unknown quantum channel based on the measurement results of the corresponding QPT experiment. The method uses the improved version of the expression for confidence levels for the case of several positive operator-valued measures (POVMs). We then demonstrate how confidence polytopes can be employed for calculating confidence intervals for affine functions of quantum states (Choi matrices), such as fidelities and observables mean values, which are used both in QST and QPT settings. As we propose, this problem can be efficiently solved using linear programming tools. We also study the performance and scalability of the developed approach on the basis of simulation and experimental data collected using IBM cloud quantum processor.