It is well known that electromagnetic computations are computationally demanding. Interestingly, many such problems can be recast to be solved by quantum annealing. Quantum annealing, a kind of quantum computer, utilizes quantum tunneling for state transitions, which enables one to find the global minimum in a complex energy landscape. Part I of this article explains quantum annealing for the classical electromagnetic community, assuming little knowledge of quantum theory. It reviews the basic principle and recent advances in quantum annealing to extend its applications, such as a hybrid quantum-classical annealing algorithm. Part II presents various examples of electromagnetic problems that can be solved by quantum annealing. These are 1) optimization of a reconfigurable directional metasurface, 2) finding current distribution in an arbitrary wire antenna, 3) finding charge and field distributions in a static condition, and 4) optimization of source excitation to focus fields in hyperthermia. Lastly, the performance of the quantum annealer is compared with classical solvers to deduce the type of applications in which a quantum annealer of current technologies can be preferred in practice.
It is well known that electromagnetic computations are computationally demanding. Interestingly, many such problems can be recast to be solved by quantum annealing. Quantum annealing, a kind of quantum computer, utilizes quantum tunneling for state transitions, which enables one to find the global minimum in a complex energy landscape. Part I of this article explains quantum annealing for the classical electromagnetic community, assuming little knowledge of quantum theory. It reviews the basic principle and recent advances in quantum annealing to extend its applications, such as a hybrid quantum-classical annealing algorithm. Part II presents various examples of electromagnetic problems that can be solved by quantum annealing. These are 1) optimization of a reconfigurable directional metasurface, 2) finding current distribution in an arbitrary wire antenna, 3) finding charge and field distributions in a static condition, and 4) optimization of source excitation to focus fields in hyperthermia. Lastly, the performance of the quantum annealer is compared with classical solvers to deduce the type of applications in which a quantum annealer of current technologies can be preferred in practice.
It is well known that electromagnetic computations are computationally demanding. Interestingly, many such problems can be recast to be solved by quantum annealing. Quantum annealing, a kind of quantum computer, utilizes quantum tunneling for state transitions, which enables one to find the global minimum in a complex energy landscape. Part I of this article explains quantum annealing for the classical electromagnetic community, assuming little knowledge of quantum theory. Both the basic principle and recent developments to extend its applications, such as hybrid quantum–classical annealing, are reviewed. Part II presents various examples of electromagnetic problems that can be solved by quantum annealing. Those are 1) optimization of a reconfigurable directional metasurface, 2) finding current distribution in an arbitrary wire antenna, 3) finding charge and field distributions in a static condition, and 4) optimization of source excitation to focus fields in hyperthermia. Finally, the performance of quantum annealer is compared with classical solvers to deduce the type of application in which a quantum annealer of current technologies can be preferred in practice.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
Quantum annealing (QA) algorithm is a new quantum optimization algorithm based on the classical simulated annealing (SA) algorithm. Unlike classical SA algorithm, which uses the thermal waves to search for the optimal solution, the QA algorithm uses the quantum tunneling effect to allow a quantum to penetrate a potential barrier with a higher energy than itself. Therefore, the algorithm can get rid of the local extreme values and is more likely to approach the global optimal with higher probability. In the literature, the QA algorithm has shown perfect optimization effects on combinatorial optimization problems. In this paper, the basic concepts and application fields of QA algorithm, which is the core principle of D-Wave quantum computer, are systematically reviewed. The applications of QA algorithm in cryptography, traveling salesman problem, graph coloring problem, and traffic path are discussed in detail. In addition, the direction of future research for QA algorithm is explored.
Combinatorial optimization is a foundation of numerous scientific, industrial, and social decision-making questions, but its usefulness is mostly restricted by the exponential complexity of the problem of classical computability. The quantum annealing (QA) has become one of the leading analogue quantum systems to address such problems, whereby optimization problems are converted into physical energy structures and quantum fluctuations are utilized to perform systematic exploration. It provides a critical, synthesized, and comprehensive review of quantum annealing as applied to combinatorial optimization, including the theoretical basis, hardware designs, algorithm methods, issues of embedding and encoding, benchmarking procedures, applications, and integration with quantum algorithms based on gates and solvers on a classical computer. We build a comprehensive taxonomy between adiabatic dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to state-of-the-art flux-qubit annealers, new architectures, and hybrid quantum classical pipelines. We show that the overhead of embedding and encoding and the benchmarking approach taken are the most significant factors in determining scalability and performance, but not the raw number of qubits. Transportation, energy systems, robotics, finance, pharmacological discovery, and machine learning are just some examples of the domain-specific case studies that use QA with minimal empirical utility as a hybrid refinement engine and not an independent solver. Moreover, we introduce a stringent evaluation of the existing benchmarking culture, clarify the causal links between QA and QAOA as well as between VQE and structural predicaments, and reveal the institutional roots of the existing restrictions. We conclude by identifying a research roadmap in the future, focusing on the annealing hardness characterization, Stoquastic control manipulation, embedding rules automation, architecture design, and development of principled quantum advantage. It creates a benchmark reference to those in the field and research and deployment of scalable, reliable, and application-relevant quantum optimization
This thesis studies several aspects of the quantum annealing (QA) computing approach. Quantum annealers' primary objective is to solve hard computational optimization problems. Because these optimization problems are in the NP-Hard complexity class, they are of great interest in several fields. One of the leading open questions concerning quantum annealers asks whether they will outperform other classical methods for solving these problems; Some aspects of this question are addressed in this thesis. The first part of the thesis investigates whether quantum annealing provides improved performance for solving a particular family of NP problems, called the Quadratic Knapsack Problem (QKP), using the D-Wave Quantum Annealer. The performance metrics used to assess QKP solving are the solution quality and the total runtime, and are benchmarked against other classical solvers. \n \nFurthermore, we extend our research on quantum annealers to propose two use cases for such systems. One is for Blockchain technology, and the second is in the area of quantum chaos. For the first use case of QA, an application for Blockchain's Proof of Work (PoW) is proposed, based on having hard optimization problems as an alternative to PoW hashing challenge, and using quantum annealers as solvers. For the second use case of QA, we propose simulating quantum chaos on the D-Wave Quantum Annealer to study the transition between the deep quantum realm and the classical limit in a chaotic system, and obtain insights into the “quantumness" of quantum annealers.
Optimization algorithms for combinatorial problems play a critical role in a wide range of applications, from logistics and scheduling to cryptography and artificial intelligence. Traditional classical methods, such as simulated annealing, genetic algorithms, and branch-and-bound techniques, have been widely employed to solve these problems, but they often face limitations in terms of computational efficiency and scalability as problem complexity grows. In recent years, quantum computing has emerged as a promising alternative, with quantum annealing offering a novel approach to solving combinatorial optimization problems. This study provides a comparative analysis of quantum annealing and classical optimization methods, highlighting their respective strengths and limitations. We explore how quantum annealing, through leveraging quantum tunnelling and superposition, has the potential to outperform classical algorithms in specific problem domains and Noisy Mean Field Annealing (NMFA) is used to comparisons of all algorithms. Benchmarking various combinatorial problems, such as the Traveling Salesman Problem (TSP), Max-Cut, Knapsack, and Quadratic Assignment Problem (QAP), this paper discusses performance metrics, computational time, and scalability. The findings suggest that while classical methods remain robust and practical for many real-world problems, quantum annealing holds significant promise, especially as quantum hardware continues to mature. However, there remain challenges in terms of noise, coherence, and problem mapping, which currently limit the full realization of quantum annealing's potential. This study offers insights into the future directions of optimization techniques and the evolving role of quantum computing in solving complex combinatorial problems.