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Mathematics
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Advances in Quantum Artificial Intelligence and Machine Learning
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Advances in Quantum Artificial Intelligence and Machine Learning

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 22668

Special Issue Editors

Prof. Dr. Andreas (Andrzej) Wichert

E-Mail Website
Guest Editor
Department of Computer Science and Engineering (DEI), Technical University of Lisbon, 2744-016 Porto Salvo, Portugal
Interests: machine learning; artificial intelligence; quantum computing
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Moret-Bonillo Vicente

E-Mail Website
Guest Editor
Centre for Information and Communications Technology Research, Department of Computer Science and Information Technologies, University of A Coruña, 15071 A Coruña, Spain
Interests: artificial intelligence in medicine; uncertainty and reasoning; intelligent monitoring systems;knowledge engineering; quantum computing
Prof. Dr. Antonio Chella

E-Mail Website
Guest Editor
RoboticsLab, Dipartimento di Ingegneria, Università degli Studi di Palermo, Viale delle Scienze ed. 6 - 90128 Palermo, Italy
Interests: machine consciousness; cognitive robotics; quantum computing; computational creativity; artificial intelligence; cognitive architectures

Special Issue Information

Dear Colleagues,

Quantum artificial intelligence will change the way we are looking at the world.  Quantum symbolical AI algorithms on a quantum computer will be faster because they can simultaneously encode many inputs of a problem and perform the calculation on all inputs in the time it takes to do one of the calculations classically. However, the solution cannot be accessed without additional costs.

The use quantum coprocessors for extensive and non tractable computation routines in AI will lead to new machine learning and artificial intelligence  applications.

Linear algebra-based quantum machine learning is based on quantum gates that describe quantum basic linear algebra subroutines. These subroutines exhibit theoretical exponential speedups compared to classical counterparts and are essential for machine learning. Quantum annealing solves optimization problems.

Quantum-Inspired machine learning and AI algorithms are based on  mathematical quantum theory to model the algorithms.

Quantum cognition uses a mathematical quantum theory to model cognitive phenomena.

clues from psychology indicate that human cognition is not only based on traditional probability theory as explained by Kolmogorov’s axioms but additionally on quantum probability.

Submissions may include original research articles or comprehensive reviews related to the topic.

Prof. Dr. Andreas (Andrzej) Wichert
Prof. Dr. Moret-Bonillo Vicente
Prof. Dr. Antonio Chella
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

  • Quantum Artificial Intelligence
  • Quantum Machine Learning
  • Quantum Cognition
  • Quantum-Inspired Algorithms

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Published Papers (6 papers)

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Research

28 pages, 1665 KiB  
Article
Quantum Tree Search with Qiskit
by Andreas Wichert
Mathematics 2022, 10(17), 3103; https://doi.org/10.3390/math10173103 - 29 Aug 2022
Viewed by 3409
Abstract
We indicate the quantum tree search qiskit implementation by popular examples from symbolical artificial intelligence, the 3-puzzle, 8-puzzle and the ABC blocks world. Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits and algorithms [...] Read more.
We indicate the quantum tree search qiskit implementation by popular examples from symbolical artificial intelligence, the 3-puzzle, 8-puzzle and the ABC blocks world. Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits and algorithms from IBM. The objects are represented by symbols and adjectives. Two principles are presented. Either the position description (adjective) is fixed and the class descriptors moves (is changed) or, in the reverse interpretation, the class descriptor is fixed and the position descriptor (adjective) moves (is changed). We indicate how to decompose the permutation operator that executes the rules by the two principles. We demonstrate that the the branching factor is reduced by Grover’s amplification to the square root of the average branching factor and not to the maximal branching factor as previously assumed. Full article
(This article belongs to the Special Issue Advances in Quantum Artificial Intelligence and Machine Learning)
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29 pages, 2642 KiB  
Article
A Quantum Planner for Robot Motion
by Antonio Chella, Salvatore Gaglio, Giovanni Pilato, Filippo Vella and Salvatore Zammuto
Mathematics 2022, 10(14), 2475; https://doi.org/10.3390/math10142475 - 16 Jul 2022
Cited by 17 | Viewed by 3335
Abstract
The possibility of integrating quantum computation in a traditional system appears to be a viable route to drastically improve the performance of systems endowed with artificial intelligence. An example of such processing consists of implementing a teleo-reactive system employing quantum computing. In this [...] Read more.
The possibility of integrating quantum computation in a traditional system appears to be a viable route to drastically improve the performance of systems endowed with artificial intelligence. An example of such processing consists of implementing a teleo-reactive system employing quantum computing. In this work, we considered the navigation of a robot in an environment where its decisions are drawn from a quantum algorithm. In particular, the behavior of a robot is formalized through a production system. It is used to describe the world, the actions it can perform, and the conditions of the robot’s behavior. According to the production rules, the planning of the robot activities is processed in a recognize–act cycle with a quantum rule processing algorithm. Such a system aims to achieve a significant computational speed-up. Full article
(This article belongs to the Special Issue Advances in Quantum Artificial Intelligence and Machine Learning)
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11 pages, 320 KiB  
Article
Categories, Quantum Computing, and Swarm Robotics: A Case Study
by Maria Mannone, Valeria Seidita and Antonio Chella
Mathematics 2022, 10(3), 372; https://doi.org/10.3390/math10030372 - 25 Jan 2022
Cited by 17 | Viewed by 5197
Abstract
The swarms of robots are examples of artificial collective intelligence, with simple individual autonomous behavior and emerging swarm effect to accomplish even complex tasks. Modeling approaches for robotic swarm development is one of the main challenges in this field of research. Here, we [...] Read more.
The swarms of robots are examples of artificial collective intelligence, with simple individual autonomous behavior and emerging swarm effect to accomplish even complex tasks. Modeling approaches for robotic swarm development is one of the main challenges in this field of research. Here, we present a robot-instantiated theoretical framework and a quantitative worked-out example. Aiming to build up a general model, we first sketch a diagrammatic classification of swarms relating ideal swarms to existing implementations, inspired by category theory. Then, we propose a matrix representation to relate local and global behaviors in a swarm, with diagonal sub-matrices describing individual features and off-diagonal sub-matrices as pairwise interaction terms. Thus, we attempt to shape the structure of such an interaction term, using language and tools of quantum computing for a quantitative simulation of a toy model. We choose quantum computing because of its computational efficiency. This case study can shed light on potentialities of quantum computing in the realm of swarm robotics, leaving room for progressive enrichment and refinement. Full article
(This article belongs to the Special Issue Advances in Quantum Artificial Intelligence and Machine Learning)
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21 pages, 597 KiB  
Article
Quantum Computing for Dealing with Inaccurate Knowledge Related to the Certainty Factors Model
by Vicente Moret-Bonillo, Samuel Magaz-Romero and Eduardo Mosqueira-Rey
Mathematics 2022, 10(2), 189; https://doi.org/10.3390/math10020189 - 8 Jan 2022
Cited by 2 | Viewed by 2619
Abstract
In this paper, we illustrate that inaccurate knowledge can be efficiently implemented in a quantum environment. For this purpose, we analyse the correlation between certainty factors and quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point [...] Read more.
In this paper, we illustrate that inaccurate knowledge can be efficiently implemented in a quantum environment. For this purpose, we analyse the correlation between certainty factors and quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point of view. Next, we introduce some basic aspects of quantum computing, and we pay special attention to quantum rule-based systems. In this context, a specific use case was built: an inferential network for testing the behaviour of the certainty factors approach in a quantum environment. After the design and execution of the experiments, the corresponding analysis of the obtained results was performed in three different scenarios: (1) inaccuracy in declarative knowledge, or imprecision, (2) inaccuracy in procedural knowledge, or uncertainty, and (3) inaccuracy in both declarative and procedural knowledge. This paper, as stated in the conclusions, is intended to pave the way for future quantum implementations of well-established methods for handling inaccurate knowledge. Full article
(This article belongs to the Special Issue Advances in Quantum Artificial Intelligence and Machine Learning)
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11 pages, 1098 KiB  
Article
Quantum-Like Sampling
by Andreas Wichert
Mathematics 2021, 9(17), 2036; https://doi.org/10.3390/math9172036 - 24 Aug 2021
Viewed by 2116
Abstract
Probability theory is built around Kolmogorov’s axioms. To each event, a numerical degree of belief between 0 and 1 is assigned, which provides a way of summarizing the uncertainty. Kolmogorov’s probabilities of events are added, the sum of all possible events is one. [...] Read more.
Probability theory is built around Kolmogorov’s axioms. To each event, a numerical degree of belief between 0 and 1 is assigned, which provides a way of summarizing the uncertainty. Kolmogorov’s probabilities of events are added, the sum of all possible events is one. The numerical degrees of belief can be estimated from a sample by its true fraction. The frequency of an event in a sample is counted and normalized resulting in a linear relation. We introduce quantum-like sampling. The resulting Kolmogorov’s probabilities are in a sigmoid relation. The sigmoid relation offers a better importability since it induces the bell-shaped distribution, it leads also to less uncertainty when computing the Shannon’s entropy. Additionally, we conducted 100 empirical experiments by quantum-like sampling 100 times a random training sets and validation sets out of the Titanic data set using the Naïve Bayes classifier. In the mean the accuracy increased from 78.84% to 79.46%. Full article
(This article belongs to the Special Issue Advances in Quantum Artificial Intelligence and Machine Learning)
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20 pages, 1720 KiB  
Article
DMO-QPSO: A Multi-Objective Quantum-Behaved Particle Swarm Optimization Algorithm Based on Decomposition with Diversity Control
by Qi You, Jun Sun, Feng Pan, Vasile Palade and Bilal Ahmad
Mathematics 2021, 9(16), 1959; https://doi.org/10.3390/math9161959 - 16 Aug 2021
Cited by 14 | Viewed by 2969
Abstract
The decomposition-based multi-objective evolutionary algorithm (MOEA/D) has shown remarkable effectiveness in solving multi-objective problems (MOPs). In this paper, we integrate the quantum-behaved particle swarm optimization (QPSO) algorithm with the MOEA/D framework in order to make the QPSO be able to solve MOPs effectively, [...] Read more.
The decomposition-based multi-objective evolutionary algorithm (MOEA/D) has shown remarkable effectiveness in solving multi-objective problems (MOPs). In this paper, we integrate the quantum-behaved particle swarm optimization (QPSO) algorithm with the MOEA/D framework in order to make the QPSO be able to solve MOPs effectively, with the advantage of the QPSO being fully used. We also employ a diversity controlling mechanism to avoid the premature convergence especially at the later stage of the search process, and thus further improve the performance of our proposed algorithm. In addition, we introduce a number of nondominated solutions to generate the global best for guiding other particles in the swarm. Experiments are conducted to compare the proposed algorithm, DMO-QPSO, with four multi-objective particle swarm optimization algorithms and one multi-objective evolutionary algorithm on 15 test functions, including both bi-objective and tri-objective problems. The results show that the performance of the proposed DMO-QPSO is better than other five algorithms in solving most of these test problems. Moreover, we further study the impact of two different decomposition approaches, i.e., the penalty-based boundary intersection (PBI) and Tchebycheff (TCH) approaches, as well as the polynomial mutation operator on the algorithmic performance of DMO-QPSO. Full article
(This article belongs to the Special Issue Advances in Quantum Artificial Intelligence and Machine Learning)
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