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arXiv:2307.02890 · Laser Physics Letters

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

Yu. I. Bogdanov, I. A. Dmitriev, B. I. Bantysh, Nadezhda A. Bogdanova, Vladimir F. Lukichev

Published May 5, 2023• 5 citations
arXivHTMLPDF

Abstract

Abstract We develop a new method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of 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, detector dark counts, 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.

DOI
10.1088/1612-202x/accf79

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Abstract We develop a new method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of 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, detector dark counts, 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.
The present work is devoted to the development of a method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of the states of a logical value 0 and a logical value 1. In the considered ion qubits, the identification of the quantum state is achieved by measuring the fluorescence of the ion by repeated excitation of the cyclic transition, which includes only the lower energy state that sets a logical value 0 and becomes bright, but does not include the upper metastable state that remains dark and sets logical value 1. It is important to note that it is not always possible to achieve low levels of registration errors due to the finite lifetime of excited levels, photon scattering, dark noise, low numerical aperture values, etc. However, even under such conditions, with use of the model of fuzzy quantum measurements, it is possible to provide precise control of quantum states. We show that a model that is characterized by relatively high levels of errors under conditions, where we have a reliable statistical model of their occurrence, is more accurate than the case when the considered errors are small, but we do not have an adequate statistical model for the occurrence of these errors. In the given illustrative examples, we show that the factor of reducing the loss of accuracy with the use of the model of fuzzy measurements can reach values of the order of 1000 or more in comparison with standard measurements. The obtained results are essential for the development of high-precision methods for controlling the technology of quantum computing on the ion platform.
The present work is devoted to the development of a method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of the states of a logical value 0 and a logical value 1. In the considered ion qubits, the identification of the quantum state is achieved by measuring the fluorescence of the ion by repeated excitation of the cyclic transition, which includes only the lower energy state that sets a logical value 0 and becomes bright, but does not include the upper metastable state that remains dark and sets logical value 1. It is important to note that it is not always possible to achieve low levels of registration errors due to the finite lifetime of excited levels, photon scattering, dark noise, low numerical aperture values, etc. However, even under such conditions, with use of the model of fuzzy quantum measurements, it is possible to provide precise control of quantum states. We show that a model that is characterized by relatively high levels of errors under conditions, where we have a reliable statistical model of their occurrence, is more accurate than the case when the considered errors are small, but we do not have an adequate statistical model for the occurrence of these errors. In the given illustrative examples, we show that the factor of reducing the loss of accuracy with the use of the model of fuzzy measurements can reach values of the order of 1000 or more in comparison with standard measurements. The obtained results are essential for the development of high-precision methods for controlling the technology of quantum computing on the ion platform.
Abstract Quantum tomography makes it possible to obtain a comprehensive information about certain logical elements of a quantum computer. In this regard, it is a promising tool for debugging quantum computers. The practical application of tomography, however, is still limited by systematic measurement errors. Their main source are errors in the quantum state preparation and measurement procedures. In this work, we investigate the possibility of suppressing these errors in the case of trapped-ion-based qudits. First, we will show that one can construct a quantum tomography protocol that contains no more than a single quantum operation in each measurement circuit. Such a protocol is more robust to errors than the measurements in mutually unbiased bases, where the number of operations increases in proportion to the square of the qudit dimension. After that, we will demonstrate the possibility of determining and accounting for the state initialization and readout errors. Together, the measures described can significantly improve the accuracy of quantum tomography of real ion-based qudits.
Abstract A method for quantum-process reconstruction using fuzzy measurement operators has been developed, where readout errors and decoherence of an ion-trap quantum register are incorporated into the effective measurement operators. The proposed approach outperforms standard methods that neglect measurement errors and decoherence in accurately reconstructing the Mølmer–Sørensen gate. Numerical experiments with entangled two-qubit states confirm that the proposed model significantly improves the fidelity of quantum process reconstruction. The obtained results demonstrate the potential of the proposed approach for creating more reliable and precise control methods in quantum computing on an ion platform, which is important for the development of quantum computing technologies.
Abstract A model for calculating quantum tomography protocols of ionic qudits is proposed, which allows taking into account errors in setting transformation parameters during measurements. The fidelity of ionic qudit tomography under errors in specifying transformation parameters is compared between the standard method and the method of fuzzy quantum measurements. A radical advantage of the fuzzy quantum measurement model over the standard model is demonstrated. It is shown that the developed model makes it possible to obtain a set of two-level of quantum state transformations of qudits that ensures the implementation of the given quantum measurement protocol.