Practical, Reliable Error Bars in Quantum Tomography

TL;DR

This paper introduces a practical and robust method for quantifying error bars in quantum tomography, using a novel representation called quantum error bars that is concise, intuitive, and useful for confidence region construction.

Contribution

The authors propose a new representation called quantum error bars for error analysis in quantum tomography, improving practicality and interpretability over existing methods.

Findings

Successfully applied to experimental data from superconducting qubits.

Provides a concise and intuitive way to estimate error spread.

Enables construction of confidence regions with a new algorithm.

Abstract

Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis. Promising recent methods based on confidence regions are difficult to apply in practice or yield error bars which are unnecessarily large. Here, we propose a practical yet robust method for obtaining error bars. We do so by introducing a novel representation of the output of the tomography procedure, the "quantum error bars". This representation is (i) concise, being given in terms of few parameters, (ii) intuitive, providing a fair idea of the "spread" of the error, and (iii) useful, containing the necessary information for constructing confidence regions. The statements resulting from our method are formulated in terms of a figure of merit, such as the fidelity to a reference state. We present an algorithm for computing this representation and provide ready-to-use software. Our procedure is applied to actual experimental data obtained from two superconducting qubits in an entangled state, demonstrating the applicability of our method.