High-precision tomography of ion qubits based on registration of fluorescent photons

TL;DR

This paper introduces a fuzzy measurement-based tomography method for ion qubits that improves state reconstruction accuracy under conditions of limited state distinguishability, accounting for systematic measurement errors.

Contribution

The authors develop a novel fuzzy measurement model and a comprehensive reconstruction algorithm that enhances quantum state tomography accuracy for ion qubits.

Findings

Higher accuracy in quantum state reconstruction compared to threshold-based models

The fuzzy measurement model captures more information about the qubit state

The method accounts for systematic measurement errors

Abstract

We develop a new method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of its logical states. It is not always possible to achieve low error rates during the readout of the quantum states of ion qubits due to the finite lifetime of excited levels, photon scattering, dark noise, low numerical aperture, etc. However, the model of fuzzy quantum measurements makes it possible to ensure precise tomography of quantum states. To do this, we developed a fuzzy measurement model based on counting the number of fluorescent photons. A statistically adequate algorithm for the reconstruction of quantum states of ion qubit registers based on fuzzy measurement operators is proposed. The algorithm uses the complete information available in the experiment and makes it possible to account for systematic measurement errors associated with the limited distinguishability of the logical states of ion qubits. We show that the developed model, although computationally more complex, contains significantly more information about the state of the qubit and provides a higher accuracy of state reconstruction compared to the model based on the threshold algorithm.