Solving larger-sized problems is an important area of research in quantum computing. Designing hybrid quantumclassical algorithms is a promising approach to solving this. We discuss decomposition-based hybrid approaches for solving optimization problems and demonstrate them for applications related to community detection.
In this thesis, we aim to answer one research question: What is the algorithmic role of classical computing in scaling up quantum computing applicability? Quantum computers have promising potential in offering more efficient solutions to some of the most demanding computational problems in the industry. There has been phenomenal progress in the theory and realization of quantum computers in the last few decades. However, quantum computing is a nascent field of technology and scaling up its computing capacity remains impeded by many open engineering/scientific challenges. One emerging solution to alleviate some of the present limitations is finding clever use of classical pre- and post-processing techniques in tandem with quantum algorithms. This helps to advantageously use scarce quantum computing resources for only a portion of a problem that benefits the most from a quantum computer. In other words, it leads to a hybrid framework in which quantum computers are considered special-purpose co-processors for accelerating specific computational tasks. We aim to develop a hybrid theoretical framework for the role of classical algorithms in scaling up quantum computing. We investigate this by focusing on three distinct limitations. We review each limitation in the context of a different application and propose an original hybrid classical-quantum solution to it. First, we focus on classical algorithms' role in a more resource-efficient compilation and embedding of quantum programs. We propose a classical algorithm that helps to embed larger optimization problems in a quantum annealer. Then we explore how a problem decomposition technique and preprocessing of the input problem can help solve significantly larger optimization problems on a quantum computer. Finally, we propose a completely hybrid quantum algorithm for preparing ground states of quantum Hamiltonians. We achieve orders of magnitude faster convergence by combining classical optimization with variational quantum state preparation.
Rising quantum technologies undertake to provide new strategies for solving hard combinatorial problems. Community detection is a fundamental issue in network studies with applications in various complex systems. A review of methods proposed in the last years in the context of quantum optimization and quantum-inspired metaheuristics to detect communities in networks is presented. Quantum optimization is introduced by recalling the main available computation models and the most popular hybridization approaches. The advantages and limitations of methods based on quantum computing and evolutionary computing are discussed.
Quantum computers acting as ML accelerators have attracted considerable interest as a promising avenue for addressing the limitations of classical computing confronted with solving complex, high-dimensional problems and handling large data sets. The most exciting aspect of quantum computing lies in its quantum advantage via techniques such as quantum parallelism, superposition, and entanglement which allows not only for rapid data processing, but also a means to resolve complex optimization problems beyond the capacity of classical algorithms. Nevertheless, the usage of quantum computing in machine learning is still a fledgling domain, with challenges concerning quantum noise, hardware restrictions, and algorithmic development. In particular, this research is concerned with the development of and study on hybrid quantum-classical algorithms that target to improve ML models in terms of computational capabilities by making use of the best of both worlds. To address this, researchers are developing hybrid algorithms that leverage the strengths of quantum computing for specific tasks, like optimization and pattern recognition, while still relying on classical computing for more flexible and larger-scale processing, ultimately achieving more efficient machine learning systems that can handle large datasets and complex problem-solving more effectively. It includes potential hybrid approaches like quantum-enhanced optimization algorithms, quantum neural networks, and quantum support vector machines, and examines how such algorithms can be used for practical ML problems including data classification, regression and clustering. Furthermore, the paper proposes that hybrid quantum algorithms offer several advantages over their classical counterparts, such as faster convergence rates, higher accuracy in high-dimensional spaces, and improved handling of non-linear and complex problem landscapes. Key advancements in the area of data processing speed and efficiency in problem-solving with and without quantum in the machine learning workflow are also highlighted in the research through comparative analysis and simulation studies. Lastly, the paper concludes by outlining the obstacles yet to be surmounted and the opportunities that lie ahead for hybrid quantum-classical algorithms, such as further improvement of quantum hardware and error mitigation methods, as well as the design of new algorithmic paradigms that seamlessly integrates the classical and quantum computing spaces.
Quantum computing, as an emerging computing paradigm, is expected to tackle problems such as quantum chemistry, optimization, quantum chemistry, information security, and artificial intelligence, which are intractable with using classical computing. Quantum computing hardware and software continue to develop rapidly, but they are not expected to realize universal quantum computation in the next few years. Therefore, the use of quantum hardware to solve practical problems in the near term has become a hot topic in the field of quantum computing. Exploration of the applications of near-term quantum hardware is of great significance in understanding the capability of quantum hardware and promoting the practical process of quantum computing. Hybrid quantum-classical algorithm (also known as variational quantum algorithm) is an appropriate model for near-term quantum hardware. In the hybrid quantum-classical algorithm, classical computers are used to maximize the power of quantum devices. By combining quantum computing with machine learning, the hybrid quantum-classical algorithm is expected to achieve the first practical application of quantum computation and play an important role in the studying of quantum computing. In this review, we introduce the framework of hybrid quantum-classical algorithm and its applications in quantum chemistry, quantum information, combinatorial optimization, quantum machine learning, and other fields. We further discuss the challenges and future research directions of the hybrid quantum-classical algorithm.
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore’s law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this article, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. To demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave’s quantum annealer and IBM’s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitude larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution. Reproducibility : Our code and data are available at Reference [1].
Optimization problems are pervasive across various domains, including logistics, finance, machine learning, and operations research. Quantum computing has emerged as a promising frontier to address these challenges, offering potential speedups for certain classes of optimization tasks. This paper explores the development and application of quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), and Grover’s search algorithm, tailored for optimization. Recent advancements in hardware, hybrid quantum-classical approaches, and variational techniques have enabled practical implementations on Noisy Intermediate-Scale Quantum (NISQ) devices. Challenges such as noise, scalability, and performance limitations are also discussed. Through theoretical analysis and case studies, this work demonstrates how quantum computing can complement classical methods, paving the way for breakthroughs in solving complex optimization problems.