Mathematics

Research

Jump to: Review

18 pages, 487 KiB

Open AccessArticle

A Formulation of Structural Design Optimization Problems for Quantum Annealing

by Fabian Key and Lukas Freinberger

Mathematics 2024, 12(3), 482; https://doi.org/10.3390/math12030482 - 02 Feb 2024

Viewed by 864

Abstract

We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where [...] Read more.

We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

29 pages, 618 KiB

Open AccessArticle

A Symbolic Approach to Discrete Structural Optimization Using Quantum Annealing

by Kevin Wils and Boyang Chen

Mathematics 2023, 11(16), 3451; https://doi.org/10.3390/math11163451 - 09 Aug 2023

Cited by 2 | Viewed by 866

Abstract

With the advent of novel quantum computing technologies and the new possibilities thereby offered, a prime opportunity has presented itself to investigate the practical application of quantum computing. This work investigates the feasibility of using quantum annealing for structural optimization. The target problem [...] Read more.

With the advent of novel quantum computing technologies and the new possibilities thereby offered, a prime opportunity has presented itself to investigate the practical application of quantum computing. This work investigates the feasibility of using quantum annealing for structural optimization. The target problem is the discrete truss sizing problem—the goal is to select the best size for each truss member so as to minimize a stress-based objective function. To make the problem compatible with quantum annealing devices, the objective function must be translated into a quadratic unconstrained binary optimization (QUBO) form. This work focuses on exploring the feasibility of making this translation. The practicality of using a quantum annealer for such optimization problems is also assessed. A method is eventually established to translate the objective function into a QUBO form and have it solved by a quantum annealer. However, scaling the method to larger problems faces some challenges that would require further research to address. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

19 pages, 729 KiB

Open AccessArticle

NISQ-Ready Community Detection Based on Separation-Node Identification

by Jonas Stein, Dominik Ott, Jonas Nüßlein, David Bucher, Mirco Schönfeld and Sebastian Feld

Mathematics 2023, 11(15), 3323; https://doi.org/10.3390/math11153323 - 28 Jul 2023

Viewed by 894

Abstract

The analysis of network structure is essential to many scientific areas ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient [...] Read more.

The analysis of network structure is essential to many scientific areas ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO-based approach that only needs number-of-nodes qubits and is represented by a QUBO matrix as sparse as the input graph’s adjacency matrix. The substantial improvement in the sparsity of the QUBO matrix, which is typically very dense in related work, is achieved through the novel concept of separation nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which, upon its removal from the graph, yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept by achieving an up to 95% optimal solution quality on three established real-world benchmark datasets. This work hence displays a promising approach to NISQ-ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large-scale, real-world problem instances. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

18 pages, 841 KiB

Open AccessArticle

Finding Debt Cycles: QUBO Formulations for the Maximum Weighted Cycle Problem Solved Using Quantum Annealing

by Hendrik Künnemann and Frank Phillipson

Mathematics 2023, 11(12), 2741; https://doi.org/10.3390/math11122741 - 16 Jun 2023

Viewed by 1279

Abstract

The problem of finding the maximum weighted cycle in a directed graph map to solve optimization problems is

NP

-hard, implying that approaches in classical computing are inefficient. Here, Quantum computing might be a promising alternative. Many current approaches to the quantum computer [...] Read more.

The problem of finding the maximum weighted cycle in a directed graph map to solve optimization problems is

NP

-hard, implying that approaches in classical computing are inefficient. Here, Quantum computing might be a promising alternative. Many current approaches to the quantum computer are based on a Quadratic Unconstrained Binary Optimization (QUBO) problem formulation. This paper develops four different QUBO approaches to this problem. The first two take the starting vertex and the number of vertices used in the cycle as given, while the latter two loosen the second assumption of knowing the size of the cycle. A QUBO formulation is derived for each approach. Further, the number of binary variables required to encode the maximum weighted cycle problem with one or both assumptions for the respective approach is made explicit. The problem is motivated by finding the maximum weighted debt cycle in a debt graph. This paper compares classical computing versus currently available (hybrid) quantum computing approaches for various debt graphs. For the classical part, it investigated the Depth-First-Search (DFS) method and Simulated Annealing. For the (hybrid) quantum approaches, a direct embedding on the quantum annealer and two types of quantum hybrid solvers were utilized. Simulated Annealing and the usage of the hybrid CQM (Constrained Quadratic Model) had promising functionality. The DFS method, direct QPU, and hybrid BQM (Binary Quadratic Model), on the other hand, performed less due to memory issues, surpassing the limit of decision variables and finding the right penalty values, respectively. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

14 pages, 739 KiB

Open AccessArticle

A Depth-Progressive Initialization Strategy for Quantum Approximate Optimization Algorithm

by Xinwei Lee, Ningyi Xie, Dongsheng Cai, Yoshiyuki Saito and Nobuyoshi Asai

Mathematics 2023, 11(9), 2176; https://doi.org/10.3390/math11092176 - 05 May 2023

Cited by 5 | Viewed by 1265

Abstract

The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial variational parameters. Hence, parameter selection for QAOA becomes an active area [...] Read more.

The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial variational parameters. Hence, parameter selection for QAOA becomes an active area of research, as bad initialization might deteriorate the quality of the results, especially at great circuit depths. We first discuss the patterns of optimal parameters in QAOA in two directions: the angle index and the circuit depth. Then, we discuss the symmetries and periodicity of the expectation that is used to determine the bounds of the search space. Based on the patterns in optimal parameters and the bounds restriction, we propose a strategy that predicts the new initial parameters by taking the difference between the previous optimal parameters. Unlike most other strategies, the strategy we propose does not require multiple trials to ensure success. It only requires one prediction when progressing to the next depth. We compare this strategy with our previously proposed strategy and the layerwise strategy for solving the Max-cut problem in terms of the approximation ratio and the optimization cost. We also address the non-optimality in previous parameters, which is seldom discussed in other works despite its importance in explaining the behavior of variational quantum algorithms. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

15 pages, 1969 KiB

Open AccessArticle

Graph Generation for Quantum States Using Qiskit and Its Application for Quantum Neural Networks

by Alexandru-Gabriel Tudorache

Mathematics 2023, 11(6), 1484; https://doi.org/10.3390/math11061484 - 18 Mar 2023

Viewed by 1929

Abstract

This paper describes a practical approach to the quantum theory using the simulation and processing technology available today. The proposed project allows us to create an exploration graph so that for an initial starting configuration of the qubits, all possible states are created [...] Read more.

This paper describes a practical approach to the quantum theory using the simulation and processing technology available today. The proposed project allows us to create an exploration graph so that for an initial starting configuration of the qubits, all possible states are created given a set of gates selected by the user. For each node in the graph, we can obtain various types of information such as the applied gates from the initial state (the transition route), necessary cost, representation of the quantum circuit, as well as the amplitudes of each state. The project is designed not as an end goal, but rather as a processing platform that allows users to visualize and explore diverse solutions for different quantum problems in a much easier manner. We then describe some potential applications of this project in other research fields, illustrating the way in which the states from the graph can be used as nodes in a new interpretation of a quantum neural network; the steps of a hybrid processing chain are presented for the problem of finding one or more states that verify certain conditions. These concepts can also be used in academia, with their implementation being possible with the help of the Python programming language, the NumPy library, and Qiskit—the open-source quantum framework developed by IBM. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

27 pages, 5376 KiB

Open AccessArticle

Heart Failure Detection Using Instance Quantum Circuit Approach and Traditional Predictive Analysis

by Shtwai Alsubai, Abdullah Alqahtani, Adel Binbusayyis, Mohemmed Sha, Abdu Gumaei and Shuihua Wang

Mathematics 2023, 11(6), 1467; https://doi.org/10.3390/math11061467 - 17 Mar 2023

Cited by 3 | Viewed by 1707

Abstract

The earlier prediction of heart diseases and appropriate treatment are important for preventing cardiac failure complications and reducing the mortality rate. The traditional prediction and classification approaches have resulted in a minimum rate of prediction accuracy and hence to overcome the pitfalls in [...] Read more.

The earlier prediction of heart diseases and appropriate treatment are important for preventing cardiac failure complications and reducing the mortality rate. The traditional prediction and classification approaches have resulted in a minimum rate of prediction accuracy and hence to overcome the pitfalls in existing systems, the present research is aimed to perform the prediction of heart diseases with quantum learning. When quantum learning is employed in ML (Machine Learning) and DL (Deep Learning) algorithms, complex data can be performed efficiently with less time and a higher accuracy rate. Moreover, the proposed ML and DL algorithms possess the ability to adapt to predictions with alterations in the dataset integrated with quantum computing that provides robustness in the earlier detection of chronic diseases. The Cleveland heart disease dataset is being pre-processed for the checking of missing values to avoid incorrect predictions and also for improvising the rate of accuracy. Further, SVM (Support Vector Machine), DT (Decision Tree) and RF (Random Forest) are used to perform classification. Finally, disease prediction is performed with the proposed instance-based quantum ML and DL method in which the number of qubits is computed with respect to features and optimized with instance-based learning. Additionally, a comparative assessment is provided for quantifying the differences between the standard classification algorithms with quantum-based learning in order to determine the significance of quantum-based detection in heart failure. From the results, the accuracy of the proposed system using instance-based quantum DL and instance-based quantum ML is found to be 98% and 83.6% respectively. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

Review

Jump to: Research

18 pages, 303 KiB

Open AccessReview

Quantum Computing in Telecommunication—A Survey

by Frank Phillipson

Mathematics 2023, 11(15), 3423; https://doi.org/10.3390/math11153423 - 06 Aug 2023

Cited by 2 | Viewed by 2795

Abstract

Quantum computing, an emerging paradigm based on the principles of quantum mechanics, has the potential to revolutionise various industries, including Telecommunications. This paper explores the transformative impact of quantum computing on the telecommunication market, focusing on its applications in solving computationally intensive problems. [...] Read more.

Quantum computing, an emerging paradigm based on the principles of quantum mechanics, has the potential to revolutionise various industries, including Telecommunications. This paper explores the transformative impact of quantum computing on the telecommunication market, focusing on its applications in solving computationally intensive problems. By leveraging the inherent properties of quantum systems, such as superposition and entanglement, quantum computers offer the promise of exponential computational speedup and enhanced problem-solving capabilities. This paper provides an in-depth analysis of the current state of quantum computing in telecommunication, examining key algorithms and approaches, discussing potential use cases, and highlighting the challenges and future prospects of this disruptive technology. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Advances in Quantum Computing and Applications

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (8 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI