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Axioms
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Computational Aspects of Machine Learning and Quantum Computing
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Computational Aspects of Machine Learning and Quantum Computing

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (26 January 2024) | Viewed by 4721

Special Issue Editor

Dr. Mariam Zomorodi

E-Mail Website
Guest Editor
Department of Computer Science, Cracow University of Technology, 31-155 Kraków, Poland
Interests: quantum computing; machine learning; deep learning; quantum machine learning

Special Issue Information

Dear Colleagues,

Machine learning and, in particular, deep learning have become the most powerful tools used to provide intelligent solutions to many complex problems. On the other hand, quantum computing has emerged as a promising technology for future computing that will solve certain problems much faster and is anticipated to revolutionize the way we address computing. Quantum computers have the potential to generate better results and enhance the performance of machine learning tasks. As a result and thanks to the advancements in both fields, the integration of these two fields has attracted great attention in recent years. More importantly, these fields share a common mathematical discipline, linear algebra, as a primary computational tool that makes their combination an interesting and emerging field of study.

This Special Issue's aim is to bring together the latest theoretical and practical advances in quantum computing and machine learning algorithms and the combination of them with a focus on implementing quantum algorithms for solving machine learning problems, such as implementing the classical neural networks with quantum computation models. Efficient qubit-based encoding of data in machine learning tasks, optimization of the parameterized quantum circuits, optimization of the ansatz, quantum-inspired algorithms in deep learning, quantum circuit optimization using techniques such as ZX-calculus, and machine translation with quantum computers are of interest to this Special Issue. 

Dr. Mariam Zomorodi
Guest Editor

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. Axioms 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 2400 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

  • quantum computing
  • deep learning
  • quantum machine learning
  • quantum algorithms
  • mathematics of quantum machine learning
  • quantum linear algebra for machine learning
  • classical-quantum neural networks
  • quantum-inspired machine learning algorithms
  • quantum embedding
  • parameterized quantum circuits
  • quantum machine translation
  • quantum variational autoencoders

Published Papers (4 papers)

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Research

13 pages, 5473 KiB  
Article
ℤ2 × ℤ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks
by Zhongtian Dong, Marçal Comajoan Cara, Gopal Ramesh Dahale, Roy T. Forestano, Sergei Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev, Katia Matcheva and Eyup B. Unlu
Axioms 2024, 13(3), 188; https://doi.org/10.3390/axioms13030188 - 13 Mar 2024
Viewed by 856
Abstract
This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three [...] Read more.
This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2×Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples. Full article
(This article belongs to the Special Issue Computational Aspects of Machine Learning and Quantum Computing)
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13 pages, 782 KiB  
Article
Hybrid Quantum Vision Transformers for Event Classification in High Energy Physics
by Eyup B. Unlu, Marçal Comajoan Cara, Gopal Ramesh Dahale, Zhongtian Dong, Roy T. Forestano, Sergei Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev and Katia Matcheva
Axioms 2024, 13(3), 187; https://doi.org/10.3390/axioms13030187 - 13 Mar 2024
Viewed by 893
Abstract
Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer [...] Read more.
Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer models could potentially alleviate this issue by reducing the training and operating time while maintaining the same predictive power. Although current quantum computers are not yet able to perform high-dimensional tasks, they do offer one of the most efficient solutions for the future. In this work, we construct several variations of a quantum hybrid vision transformer for a classification problem in high-energy physics (distinguishing photons and electrons in the electromagnetic calorimeter). We test them against classical vision transformer architectures. Our findings indicate that the hybrid models can achieve comparable performance to their classical analogs with a similar number of parameters. Full article
(This article belongs to the Special Issue Computational Aspects of Machine Learning and Quantum Computing)
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15 pages, 1476 KiB  
Article
A Comparison between Invariant and Equivariant Classical and Quantum Graph Neural Networks
by Roy T. Forestano, Marçal Comajoan Cara, Gopal Ramesh Dahale, Zhongtian Dong, Sergei Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev, Katia Matcheva and Eyup B. Unlu
Axioms 2024, 13(3), 160; https://doi.org/10.3390/axioms13030160 - 29 Feb 2024
Viewed by 952
Abstract
Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such [...] Read more.
Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, have greatly motivated the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, we can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we provide a fair and comprehensive comparison of classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their area under the curve (AUC) scores, the quantum networks were found to outperform the classical networks. However, seeing the computational advantage of quantum networks in practice may have to wait for the further development of quantum technology and its associated application programming interfaces (APIs). Full article
(This article belongs to the Special Issue Computational Aspects of Machine Learning and Quantum Computing)
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21 pages, 7032 KiB  
Article
A Modified Quantum-Inspired Genetic Algorithm Using Lengthening Chromosome Size and an Adaptive Look-Up Table to Avoid Local Optima
by Shahin Hakemi, Mahboobeh Houshmand, Seyyed Abed Hosseini and Xujuan Zhou
Axioms 2023, 12(10), 978; https://doi.org/10.3390/axioms12100978 - 17 Oct 2023
Cited by 1 | Viewed by 1265
Abstract
The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy [...] Read more.
The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases to avoid local optima and premature convergence. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm’s optimization abilities. To evaluate the effectiveness of these ideas, DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm and its superiority for solving multimodal benchmark functions and real-world constrained engineering problems. Full article
(This article belongs to the Special Issue Computational Aspects of Machine Learning and Quantum Computing)
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