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Микроэлектроника

Precise Tomography of Qudits

Yu. I. Bogdanov, Nadezhda A. Bogdanova, Yu. A. Kuznetsov, K. B. Koksharov, Vladimir F. Lukichev

Published May 1, 2023• 0 citations
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Abstract

Multilevel quantum states (qudits) represent a promising platform for scalable quantum comput-ing. In this paper, we present a method for precisely controlling such systems using fuzzy quantum measure-ments. 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 mutu-ally unbiased bases (MUBs) of various dimensions are considered. The accuracy characteristics of sets of ran-dom states uniformly distributed with respect to the Haar measure are studied.

DOI
10.31857/s0544126923700308

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Multilevel quantum states (qudits) represent a promising platform for scalable quantum comput-ing. In this paper, we present a method for precisely controlling such systems using fuzzy quantum measure-ments. 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 mutu-ally unbiased bases (MUBs) of various dimensions are considered. The accuracy characteristics of sets of ran-dom states uniformly distributed with respect to the Haar measure are studied.
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.
Abstract This work is a continuation of our research [1], aimed at developing methods for high-precision control of multilevel quantum systems (qudits). This study presents a method for precision quantum measurements of such systems using fuzzy quantum measurements. The developed method is used for precision reconstruction of quantum states under conditions of significant influence of amplitude and phase relaxation. The protocols of quantum measurements based on mutually unbiased bases of various dimensions are considered. The accuracy characteristics of sets of random states uniformly distributed with respect to the Haar measure are studied. A study was made of the dependence of the accuracy loss function on the parameters of phase and amplitude relaxation. It is shown that the results of the performed numerical experiments are in good agreement with the analytical results obtained on the basis of the universal distribution of accuracy losses using fuzzy measurement protocols.
Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly symmetric sets of state vectors, on mutually unbiased bases (MUB), and two-level transformations. Using the universal distribution for the fidelity of quantum state tomography, we estimate the fidelity and efficiency of quantum measurements for qudits of various dimensions as applied to a set of random states uniformly distributed over the Haar measure.
The report presents a general approach for estimating quantum information technologies by means of fuzzy quantum measurements. The developed methods are used for precision reconstruction of quantum states under conditions of significant influence of decoherence and quantum noise. Monitoring of the amount of information about quantum states and their parameters, including the loss of information caused by the effect of quantum noise, is considered. Examples of the developed approach as applied to readout errors and phase relaxation are presented.
Abstract We present a method for reconstructing multilevel quantum states (qudits) that explicitly accounts for readout errors. Our algorithm relies on the confusion matrix, treated as a stochastic transition matrix of a Markov chain. We pay special attention to the model with uniformly distributed errors and to the critical error probability at which the system completely loses the ability to reconstruct states. The reported results extend our earlier approach to high-precision control of qudits using fuzzy (unsharp) quantum measurements under decoherence.
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