This chapter presents the various modern optimization problem solving techniques available in literature and their limitations. Convergence speed is the primary problem of the modern optimization methods, which has been resolved by using quantum computing. IBM provided quantum computing cloud platform for all the users IBM Q Experience is considered here for field of study. It has two key features, circuit composer and QISkit. Keywords: Quantum computing, function optimization, IBM Q Experience.
This chapter presents the various modern optimization problem solving techniques available in literature and their limitations. Convergence speed is the primary problem of the modern optimization methods, which has been resolved by using quantum computing. IBM provided quantum computing cloud platform for all the users IBM Q Experience is considered here for field of study. It has two key features, circuit composer and QISkit. Keywords: Quantum computing, function optimization, IBM Q Experience.
Quantum optimization is a promising field revolutionizing problem-solving across domains. This study compares Particle Swarm Optimization (PSO), Moth Flame Optimization (MFO), and Genetic Algorithm (GA) on three platforms : a local computer, a local computer with quantum integration, and an IBM quantum machine. Results indicate PSO’s consistent performance across all setups, with the IBM quantum machine having a longer elapsed time. For MFO, the optimal solution is found using the IBM quantum machine, despite its longer execution time. Similarly, GA achieves the best results on the IBM quantum machine. These findings suggest that while quantum computers excel in solving complex problems, their execution time for simpler tasks remains higher than classical setups. Future research should address challenges like noise, limited qubits, and high material costs to improve quantum computers’ efficiency and availability.
Abstract Quantum computing has emerged as a promising field with the potential to revolutionize information processing and storage. Understanding its current state and research trajectory is crucial. This study aims to map the current literature on quantum computing, to identify how quantum computing is being used in solving quantum software problems and improving quantum algorithms. Moreover, it examines evaluation parameters and the challenges faced in this field. A systematic mapping study was conducted using the SCOPUS database, including all papers up to December 2024. Relevant articles were selected based on inclusion criteria, and a content analysis was performed to categorize and synthesize the findings. Information was gathered from 33 primary studies. Findings show that quantum computing is mainly applied in machine learning and optimization, though classical methods still outperform it. IBM Quantum is the most used platform. Research focuses on algorithm efficiency, verification over validation, and resource optimization, but lacks standardized evaluation methods. Key limitations include hardware constraints, noise, and scalability, while challenges involve integration, error correction, and problem formulation. Quantum computing continues to face significant technological challenges, but current research lays the groundwork for future advances. More practical studies on real hardware and strategies to improve the implementation and performance of quantum algorithms are needed. Effective evaluation, verification, and validation of quantum solutions must be further investigated.
Quantum computing is being increasingly adopted for solving classically intractable problems across various domains. However, the availability of accessible and scalable software frameworks remains essential for practical experimentation and adoption. IBM's open-source quantum computing toolkit 'Qiskit' has become a key player in this space by offering tools for circuit design, simulation, hardware execution, and domain-specific applications. This survey provides a systematic review of how Qiskit has evolved and what it has contributed to several critical fields including cryptography and cybersecurity, image and signal processing, climate science and energy applications, and finance. We show how Qiskit facilitates hybrid classical-quantum workflows and enables the deployment of algorithms on physical quantum hardware through error mitigation and modular integration approaches. Our exploration covers several key applications, including quantum key distribution, climate simulation, and quantum-enhanced portfolio optimization, while providing practical insights into their implementation. This work also covers the framework's technical structure and current limitations associated with scalability and reproducibility. By bringing together developments that have been scattered across different areas, this work serves as a reference point for researchers and practitioners who want to understand or contribute to Qiskit-enabled quantum computing.
Computational science is rebuilt by the various quantum foundations such as entanglement, superposition, and interference. This chapter connects the recent advances of real-world applications to quantum algorithms. Quantum computing (QC) is becoming increasingly powerful through hardware developments like International Business Machine's (IBM's) Eagle and Google's Willow. Feedback-Based Quantum Algorithms (FQAs), Variational Quantum Algorithms (VQAs), and Quantum Gibbs Sampling are deliberated. These methodologies are well-suited to noisy intermediate-scale quantum (NISQ) devices. Flow diagrams, case studies, and tables highlight the advantages of algorithms over traditional methods. The specialized algorithms and foundational algorithms, such as Shor's factoring, graph analysis-based quantum walk, are also discussed in this chapter. The chapter reviews various hardware challenges such as gate errors, limited connectivity and qubit decoherence. The chapter delves into the hybrid model and quantum classical optimization for the algorithmic issues such as circuit depth and barren plateaus. QC concepts can be addressed and experimented through various cloud platforms such as PennyLane, Amazon Braket, and IBM Quantum. The interdisciplinary approaches in bridging the gap between theory and practice are emphasized. Overall, the chapter serves as a foundational guide for practitioners in quantum technologies.
Abstract This practical guide focuses on optimization loops in variational quantum algorithms (VQAs), based on IBM Q learning resources. The exercises were performed by the author on May 4, 2024, using IBM Q cloud resources. Optimization loops are a core component of variational algorithms, enabling iterative exploration of parameterized quantum states within the ansatz to identify optimal configurations. In this lesson, participants learn to execute the optimization cycle, applying classical optimizers to the parameterized quantum circuit. Key concepts include understanding trade-offs between local and global optimization strategies, identifying and avoiding barren plateaus—regions in the parameter space where gradients vanish—and ensuring efficient convergence toward the optimal solution. The optimizer evaluates the cost function C(θ⃗)C(\vec{\theta})C(θ) at each iteration to guide the selection of the next parameter set, repeating the cycle until convergence is achieved. Upon completion, the optimal parameter set θ⃗∗\vec{\theta}^*θ∗ is returned, representing the best approximation of the target quantum state. Hands-on exercises in Qiskit enable participants to integrate parameterized ansätze, cost function evaluation, and classical optimization routines into a hybrid quantum-classical workflow. The lesson emphasizes practical strategies for balancing convergence speed, accuracy, and computational resources, illustrating the central role of optimization loops in achieving quantum advantage on noisy intermediate-scale quantum (NISQ) devices. This guide equips participants with foundational skills to implement effective optimization cycles, forming the basis for applications in quantum chemistry, combinatorial optimization, and machine learning.
Introduction. Quantum computers provide several times faster solutions to several NP-hard combinatorial optimization problems in comparison with computing clusters. The trend of doubling the number of qubits of quantum computers every year suggests the existence of an analog of Moore's law for quantum computers, which means that soon they will also be able to get a significant acceleration of solving many applied large-scale problems. The purpose of the article is to review methods for creating algorithms of quantum computer mathematics for combinatorial optimization problems and to analyze the influence of the qubit-to-qubit coupling and connections strength on the performance of quantum data processing. Results. The article offers approaches to the classification of algorithms for solving these problems from the perspective of quantum computer mathematics. It is shown that the number and strength of connections between qubits affect the dimensionality of problems solved by algorithms of quantum computer mathematics. It is proposed to consider two approaches to calculating combinatorial optimization problems on quantum computers: universal, using quantum gates, and specialized, based on a parameterization of physical processes. Examples of constructing a half-adder for two qubits of an IBM quantum processor and an example of solving the problem of finding the maximum independent set for the IBM and D-wave quantum computers are given. Conclusions. Today, quantum computers are available online through cloud services for research and commercial use. At present, quantum processors do not have enough qubits to replace semiconductor computers in universal computing. The search for a solution to a combinatorial optimization problem is performed by achieving the minimum energy of the system of coupled qubits, on which the task is mapped, and the data are the initial conditions. Approaches to solving combinatorial optimization problems on quantum computers are considered and the results of solving the problem of finding the maximum independent set on the IBM and D-wave quantum computers are given. Keywords: quantum computer, quantum computer mathematics, qubit, maximal independent set for a graph.