Currently, state-of-the-art approaches to solving complex optimization problems have focused solely on methods requiring high computational time and unable to find the global optimal solution. In this work, a methodology based on quantum computing is presented to overcome these drawbacks. The novelty of this framework stems from the quantum computer�s architecture and taking into consideration the quantum phenomena that take place to solve optimization problems with specific structure. The proposed methodology includes steps for the transformation of the initial optimization problem into an unconstrainted optimization problem with binary variables and its embedding onto a quantum device. Moreover, different resolution levels for the transformation step and different architectures for the embedding process are utilized. To illustrate the procedure, a case study based on Haverly�s pooling and blending problem is examined while demonstrating the potential of the proposed approach. The results indicate that the succinct formulation exhibited higher success rate during the embedding procedure for the different examined architectures, and the quantum annealing solver exhibited the best performance among the various solvers investigated. This highlights the potential of the approach for solving this type of problems with the rapid development and improvement of quantum hardware and expanding it to more complex chemical engineering optimization systems.
Currently, state-of-the-art approaches to solving complex optimization problems have focused solely on methods requiring high computational time and unable to find the global optimal solution. In this work, a methodology based on quantum computing is presented to overcome these drawbacks. The novelty of this framework stems from the quantum computer�s architecture and taking into consideration the quantum phenomena that take place to solve optimization problems with specific structure. The proposed methodology includes steps for the transformation of the initial optimization problem into an unconstrainted optimization problem with binary variables and its embedding onto a quantum device. Moreover, different resolution levels for the transformation step and different architectures for the embedding process are utilized. To illustrate the procedure, a case study based on Haverly�s pooling and blending problem is examined while demonstrating the potential of the proposed approach. The results indicate that the succinct formulation exhibited higher success rate during the embedding procedure for the different examined architectures, and the quantum annealing solver exhibited the best performance among the various solvers investigated. This highlights the potential of the approach for solving this type of problems with the rapid development and improvement of quantum hardware and expanding it to more complex chemical engineering optimization systems.
Industrial optimization challenges, such as the pooling and blending problem (PBP), require advanced computational methods to address non-convexity and scalability limitations in classical solvers. This work introduces a novel methodological framework for solving PBPs using quantum annealing (QA) that transforms the PBP into quadratic unconstrained binary optimization (QUBO) formulations at two resolution levels, enabling direct deployment on quantum annealers. Key innovations include a discretization technique tailored for PBP’s bilinear constraints and an embedding method optimized for current quantum hardware. Benchmarking against classical solvers focuses on Haverly’s classical three-stream PBP, enabling transparent comparison and development of quantum embedding and solution techniques. The proposed framework offers a scalable template for adapting similar engineering systems to quantum annealing architectures. Addressing genuine industrial-scale instances will require future advances in quantum hardware and embedding algorithms. The results demonstrate that QA exhibits the best performance among the examined alternatives, provide foundational insights towards leveraging QA in Process Systems Engineering.
This paper explores the application of Quantum Annealing (QA) to the field of combinatorial optimization. The core idea is to leverage the principles of quantum mechanics, specifically quantum tunneling, to efficiently solve complex optimization problems. We present a framework for utilizing QA to tackle problems represented as quadratic unconstrained binary optimization (QUBO) models. The methodology focuses on mapping the problem's constraints and objective function into a form suitable for QA hardware. We discuss the challenges involved in this mapping process, including the limitations of current QA devices and the need for careful problem formulation. Furthermore, we analyze the potential advantages of QA over classical optimization techniques, particularly concerning the exploration of a wider solution space. The research highlights the promise of QACO as a viable approach for tackling computationally demanding combinatorial optimization tasks, offering a novel method to enhance optimization efficiency.
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6561×) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.
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.
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 paper explores the application of quantum annealing to solve combinatorial optimization problems. The core idea centers around mapping these problems onto a quantum annealing platform and utilizing the quantum effects to find optimal or near-optimal solutions. Specifically, we investigate the potential of improved parameter tuning and algorithmic modifications to enhance the effectiveness of quantum annealing for problems such as the Traveling Salesperson Problem (TSP) and the Knapsack Problem. While quantum annealing has shown promise, its practical performance remains limited, and this work aims to address this limitation through targeted algorithmic and parameter optimization. The central focus is on demonstrating a method for translating a classical combinatorial problem into a suitable form for quantum annealing, followed by a strategic approach to controlling the annealing process to guide the system toward a desired solution. The efficacy of this approach is evaluated conceptually, with a focus on outlining the necessary steps and considerations for successful implementation.