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Entropy
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Methods and Applications of Quantum Data Processing
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Methods and Applications of Quantum Data Processing

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 9905

Special Issue Editors

Dr. Jaroslaw Miszczak

E-Mail Website
Guest Editor
Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland
Interests: quantum information theory; complex systems; programming languages
Prof. Dr. Zbigniew Puchała

E-Mail Website
Guest Editor
1. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, 44-100 Gliwice, Poland
2. Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
Interests: quantum information theory; geometry of quantum states; quantum control; matrix inequalities

Special Issue Information

Interest in quantum computing is motivated by the prospect of utilising the power of quantum machines for solving challenging computational problems.  This interest resulted in the development of new applications covering the possible utilisation of quantum mechanical principles in communication, data processing, and more recently in logic, game theory, artificial intelligence, and theory of programming languages.

This Special Issue aims to provide a forum for researchers from different research areas interested in applying principles of quantum mechanics in their area of specialisation. Contributions devoted to  quantum programming languages, the simulation of quantum systems, quantum-enhanced machine learning, and quantum information processing in complex systems are welcome. We encourage in-depth analyses of the use cases in the respective areas, including applications to real-world data and the modelling of industrial, financial, and sociological systems. Manuscripts devoted to demonstrating the strengths and limitations of data processing based on quantum principles of quantum mechanics are also welcome. We also encourage submissions analysing the efficiency of quantum programmes developed for current hardware platforms which take into account input data modification, imprecise implementation of the quantum procedures, or various models used on current quantum computers.

Dr. Jaroslaw Miszczak
Prof. Dr. Zbigniew Puchała
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (4 papers)

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Research

20 pages, 2456 KiB  
Article
Characterizing the Reproducibility of Noisy Quantum Circuits
by Samudra Dasgupta and Travis S. Humble
Entropy 2022, 24(2), 244; https://doi.org/10.3390/e24020244 - 05 Feb 2022
Cited by 6 | Viewed by 2129
Abstract
The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead [...] Read more.
The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits. Full article
(This article belongs to the Special Issue Methods and Applications of Quantum Data Processing)
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10 pages, 341 KiB  
Article
Relating Entropies of Quantum Channels
by Dariusz Kurzyk, Łukasz Pawela and Zbigniew Puchała
Entropy 2021, 23(8), 1028; https://doi.org/10.3390/e23081028 - 10 Aug 2021
Cited by 1 | Viewed by 1965
Abstract
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output [...] Read more.
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity. Full article
(This article belongs to the Special Issue Methods and Applications of Quantum Data Processing)
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21 pages, 4195 KiB  
Article
Switching and Swapping of Quantum Information: Entropy and Entanglement Level
by Marek Sawerwain, Joanna Wiśniewska and Roman Gielerak
Entropy 2021, 23(6), 717; https://doi.org/10.3390/e23060717 - 04 Jun 2021
Cited by 2 | Viewed by 2462
Abstract
Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information [...] Read more.
Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementary properties analysed through the prism of the concept of the entropy, are presented. As an example of the local information swapping usage, we demonstrate a certain realisation of the quantum switch. Entanglement levels, during the work of the switch, are calculated with the Negativity measure and a separability criterion based on the von Neumann entropy, spectral decomposition and Schmidt decomposition. Results of numerical experiments, during which the entanglement levels are estimated for systems under consideration with and without distortions, are presented. The noise is generated by the Dzyaloshinskii-Moriya interaction and the intrinsic decoherence is modelled by the Milburn equation. This work contains a switch realisation in a circuit form—built out of elementary quantum gates, and a scheme of the circuit which estimates levels of entanglement during the switch’s operating. Full article
(This article belongs to the Special Issue Methods and Applications of Quantum Data Processing)
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13 pages, 1510 KiB  
Article
Development of High Performance Quantum Image Algorithm on Constrained Least Squares Filtering Computation
by Shumei Wang, Pengao Xu, Ruicheng Song, Peiyao Li and Hongyang Ma
Entropy 2020, 22(11), 1207; https://doi.org/10.3390/e22111207 - 25 Oct 2020
Cited by 4 | Viewed by 1992
Abstract
Recent development of computer technology may lead to the quantum image algorithms becoming a hotspot. Quantum information and computation give some advantages to our quantum image algorithms, which deal with the limited problems that cannot be solved by the original classical image algorithm. [...] Read more.
Recent development of computer technology may lead to the quantum image algorithms becoming a hotspot. Quantum information and computation give some advantages to our quantum image algorithms, which deal with the limited problems that cannot be solved by the original classical image algorithm. Image processing cry out for applications of quantum image. Most works on quantum images are theoretical or sometimes even unpolished, although real-world experiments in quantum computer have begun and are multiplying. However, just as the development of computer technology helped to drive the Technology Revolution, a new quantum image algorithm on constrained least squares filtering computation was proposed from quantum mechanics, quantum information, and extremely powerful computer. A quantum image representation model is introduced to construct an image model, which is then used for image processing. Prior knowledge is employed in order to reconstruct or estimate the point spread function, and a non-degenerate estimate is obtained based on the opposite processing. The fuzzy function against noises is solved using the optimal measure of smoothness. On the constraint condition, determine the minimum criterion function and estimate the original image function. For some motion blurs and some kinds of noise pollutions, such as Gaussian noises, the proposed algorithm is able to yield better recovery results. Additionally, it should be noted that, when there is a noise attack with very low noise intensity, the model based on the constrained least squares filtering can still deliver good recovery results, with strong robustness. Subsequently, discuss the simulation analysis of the complexity of implementing quantum circuits and image filtering, and demonstrate that the algorithm has a good effect on fuzzy recovery, when the noise density is small. Full article
(This article belongs to the Special Issue Methods and Applications of Quantum Data Processing)
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