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arXiv:2011.04179 · Laser Physics Letters

Quantum tomography of noisy ion-based qudits

B I Bantysh, Yu I Bogdanov

Published Dec 18, 2020• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1612-202x/abca44

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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.
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and measurement errors complicates the practical use of this procedure. In this work, we investigate the possibility of estimating these errors from experiment. These estimates are subsequently used to build a robust quantum tomography model. The model allows one to accurately reconstruct unitary errors of single-qubit gates. We show that, having such imperfect single-qubit gates with pre-estimated errors, one can obtain transformations close to ideal ones. A similar approach can also significantly mitigate single-qubit gates cross-talk.
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.
Abstract Characterizing the dynamics of quantum systems is a central task for the development of quantum information processors (QIPs). It serves to benchmark different devices, learn about their specific noise, and plan the next hardware upgrades. However, this task is also very challenging, for it requires a large number of measurements and time-consuming classical processing. Moreover, when interested in the time dependence of the noise, there is an additional overhead since the characterization must be performed repeatedly within the time interval of interest. To overcome this limitation while, at the same time, ordering the learned sources of noise by their relevance, we focus on the inference of the dynamical generators of the noisy dynamics using Lindbladian quantum tomography (LQT). We propose two different improvements of LQT that alleviate previous shortcomings. In the weak-noise regime of current QIPs, we manage to linearize the maximum likelihood estimation of LQT, turning the constrained optimization into a convex problem to reduce the classical computation cost and to improve its robustness. Moreover, by introducing compressed sensing techniques, we reduce the number of required measurements without sacrificing accuracy. To illustrate these improvements, we apply our LQT tools to trapped-ion experiments of single- and two-qubit gates, advancing in this way the previous state of the art.
We propose a model for quantum tomography protocols of ion-trap qudits that incorporates parameter-setting errors in measurement transformations. A comparative analysis of reconstruction accuracy under transformation uncertainty is conducted for both the conventional projective measurement approach and the fuzzy quantum measurement framework. The results demonstrate a substantial advantage of the fuzzy measurement model in the presence of transformation inaccuracies. Furthermore, the model enables the construction of a complete set of two-level unitary transformations applicable to qudit states.
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.
Abstract Multilevel quantum states (qudits) represent a promising platform for scalable quantum computing. In this paper, we present a method for precisely controlling such systems using fuzzy quantum measurements. The developed method is used for a precise reconstruction of quantum states under conditions of a significant effect of decoherence and quantum noise. Protocols for quantum measurements based on mutually unbiased bases (MUBs) of various dimensions are considered. The accuracy characteristics of sets of random states uniformly distributed with respect to the Haar measure are studied.