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.
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.
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.
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 (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.
Abstract : One approach to solving planning problems is to compile them to another problem for which powerful off-the-shelf solvers are available; common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available: quantum annealing (QA). QA takes as input problem instances encoded as Quadratic Unconstrained Binary Optimization (QUBO). Early quantum annealers are now available, and more sophisticated quantum annealers will likely be built over the next decades. Specific quantum annealing hardware implementations have specific constraints, restricting the types of QUBOs each can take as input. In this paper, we introduce the planning community to the key steps involved in compiling planning problems to quantum annealing hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we provide preliminary results from running an early quantum annealer on a parameterized family of hard planning problems. The results show that different mappings can lead to a substantial difference in performance, even when many superficial features of the resulting instances are similar. We also provide some insights gained from this early study, and suggest directions for future work.
Abstract One approach to solving planning problems is to compile them to other problems for which powerful off-the-shelf solvers are available; common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available: quantum annealing (QA). QA takes as input problem instances of quadratic unconstrained binary optimization (QUBO) problem. Early quantum annealers are now available, though their constraints restrict the types of QUBOs they can take as input. Here, we introduce the planning community to the key steps in compiling planning problems to QA hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we describe preliminary results from running an early quantum annealer on a parametrized family of hard planning problems. The results show that different mappings can substantially affect performance, even when many features of the resulting instances are similar. We conclude with insights gained from this early study that suggest directions for future work.