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Mathematics
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Mathematical Perspectives on Quantum Computing and Communication
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Mathematical Perspectives on Quantum Computing and Communication

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 8560

Special Issue Editors

Dr. Artur Czerwinski

E-Mail Website
Guest Editor
Institute of Physics, Faculty of Physics, Astronomy and Intypeatics, Nicolaus Copernicus University in Torun, ul. Grudziadzka 5, 87-100 Torun, Poland
Interests: quantum optics; entanglement; quantum dynamics; open quantum systems; non-Markovian evolution; quantum state tomography; time-bin encoding; phase retrieval; quantum Hamiltonian tomography; tomography; entanglement measures; quantum measurement; decoherence
Special Issues, Collections and Topics in MDPI journals
Dr. Xiangji Cai

E-Mail Website
Guest Editor
School of Science, Shandong Jianzhu University, Jinan 250101, China
Interests: dynamical theory of open quantum systems; theoretical research on quantum transport and quantum measurement; condensed matter physics; theoretical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to invite you to submit your research for consideration in a Special Issue of Mathematics, focused on the latest advances in quantum information theory. The goal of this Special Issue is to showcase the latest research in this rapidly evolving field and to provide a platform for researchers to share their latest findings.

Quantum information theory is a rapidly developing field, with new breakthroughs and discoveries being made on a regular basis. This Special Issue will provide a unique opportunity for researchers to share their work and to discuss the latest developments in the field. Topics of interest include but are not limited to entanglement, quantum algorithms, quantum error correction, quantum cryptography, quantum communication, quantum computing, quantum simulation, mathematical methods, numerical modeling, and quantum machine learning and the mathematical formalism of open quantum systems. 

We encourage submissions from researchers working in all areas of quantum information theory, including experimental, theoretical, and applied research. This Special Issue aims to highlight the mathematical aspects of the field and the use of mathematical methods and numerical modeling in the study of quantum information theory. The deadline for submissions is 31 December 2023.

We look forward to receiving your submissions and to publishing a high-quality Special Issue that reflects the latest advances in quantum information theory with a strong mathematical focus.

You may choose our Joint Special Issue in AppliedMath.

Dr. Artur Czerwinski
Dr. Cai Xiangji
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. Mathematics is an international peer-reviewed open access semimonthly 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.

Keywords

  • open quantum systems
  • mathematical methods of quantum theory
  • numerical modeling and simulations
  • quantum information theory
  • quantum algorithms
  • quantum error correction
  • quantum cryptography
  • quantum communication
  • quantum computing
  • quantum simulation
  • quantum machine learning
  • quantum entanglement
  • quantum error-correction codes
  • quantum information processing
  • quantum teleportation
  • quantum key distribution
  • quantum computing architectures
  • quantum complexity theory
  • quantum control theory
  • quantum metrology
  • quantum algorithms for optimization
  • quantum supremacy
  • quantum computing algorithms
  • quantum artificial intelligence
  • quantum neural networks
  • quantum coherence
  • quantum state tomography
  • quantum foundations
  • quantum many-body systems
  • quantum supremacy experiments
  • quantum technologies

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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Research

22 pages, 684 KiB  
Article
Hybrid Quantum–Classical Neural Networks for Efficient MNIST Binary Image Classification
by Deepak Ranga, Sunil Prajapat, Zahid Akhtar, Pankaj Kumar and Athanasios V. Vasilakos
Mathematics 2024, 12(23), 3684; https://doi.org/10.3390/math12233684 - 24 Nov 2024
Viewed by 441
Abstract
Image classification is a fundamental task in deep learning, and recent advances in quantum computing have generated significant interest in quantum neural networks. Traditionally, Convolutional Neural Networks (CNNs) are employed to extract image features, while Multilayer Perceptrons (MLPs) handle decision making. However, parameterized [...] Read more.
Image classification is a fundamental task in deep learning, and recent advances in quantum computing have generated significant interest in quantum neural networks. Traditionally, Convolutional Neural Networks (CNNs) are employed to extract image features, while Multilayer Perceptrons (MLPs) handle decision making. However, parameterized quantum circuits offer the potential to capture complex image features and define sophisticated decision boundaries. In this paper, we present a novel Hybrid Quantum–Classical Neural Network (H-QNN) for image classification, and demonstrate its effectiveness using the MNIST dataset. Our model combines quantum computing with classical supervised learning to enhance classification accuracy and computational efficiency. In this study, we detail the architecture of the H-QNN, emphasizing its capability in feature learning and image classification. Experimental results demonstrate that the proposed H-QNN model outperforms conventional deep learning methods in various training scenarios, showcasing its effectiveness in high-dimensional image classification tasks. Additionally, we explore the broader applicability of hybrid quantum–classical approaches in other domains. Our findings contribute to the growing body of work in quantum machine learning, and underscore the potential of quantum-enhanced models for image recognition and classification. Full article
(This article belongs to the Special Issue Mathematical Perspectives on Quantum Computing and Communication)
38 pages, 4712 KiB  
Article
Large-Scale Simulation of Shor’s Quantum Factoring Algorithm
by Dennis Willsch, Madita Willsch, Fengping Jin, Hans De Raedt and Kristel Michielsen
Mathematics 2023, 11(19), 4222; https://doi.org/10.3390/math11194222 - 9 Oct 2023
Cited by 4 | Viewed by 4652
Abstract
Shor’s factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today’s quantum computers only permit a study of Shor’s algorithm for very small numbers. Here, we show how large GPU-based supercomputers can be used to [...] Read more.
Shor’s factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today’s quantum computers only permit a study of Shor’s algorithm for very small numbers. Here, we show how large GPU-based supercomputers can be used to assess the performance of Shor’s algorithm for numbers that are out of reach for current and near-term quantum hardware. First, we study Shor’s original factoring algorithm. While theoretical bounds suggest success probabilities of only 3–4%, we find average success probabilities above 50%, due to a high frequency of “lucky” cases, defined as successful factorizations despite unmet sufficient conditions. Second, we investigate a powerful post-processing procedure, by which the success probability can be brought arbitrarily close to one, with only a single run of Shor’s quantum algorithm. Finally, we study the effectiveness of this post-processing procedure in the presence of typical errors in quantum processing hardware. We find that the quantum factoring algorithm exhibits a particular form of universality and resilience against the different types of errors. The largest semiprime that we have factored by executing Shor’s algorithm on a GPU-based supercomputer, without exploiting prior knowledge of the solution, is 549,755,813,701 = 712,321 × 771,781. We put forward the challenge of factoring, without oversimplification, a non-trivial semiprime larger than this number on any quantum computing device. Full article
(This article belongs to the Special Issue Mathematical Perspectives on Quantum Computing and Communication)
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14 pages, 2029 KiB  
Article
Quantum Advantages of Teleportation and Dense Coding Protocols in an Open System
by Saeed Haddadi, Maryam Hadipour, Soroush Haseli, Atta Ur Rahman and Artur Czerwinski
Mathematics 2023, 11(6), 1407; https://doi.org/10.3390/math11061407 - 14 Mar 2023
Cited by 8 | Viewed by 2313
Abstract
Quantum teleportation and dense coding are well-known quantum protocols that have been widely explored in the field of quantum computing. In this paper, the efficiency of quantum teleportation and dense coding protocols is examined in two-level atoms with two-photon transitions via the Stark [...] Read more.
Quantum teleportation and dense coding are well-known quantum protocols that have been widely explored in the field of quantum computing. In this paper, the efficiency of quantum teleportation and dense coding protocols is examined in two-level atoms with two-photon transitions via the Stark shift effect, where each atom is separately coupled to a dissipative reservoir at zero temperature. Our results show that non-Markovianity and Stark shift can play constructive roles in restoring the quantum advantages of these protocols after they are diminished. These findings could offer a potential solution to preserving the computational and communicative advantages of quantum technologies. Full article
(This article belongs to the Special Issue Mathematical Perspectives on Quantum Computing and Communication)
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