Computer-aided Molecular and Process Design (CAMPD) is an equation-oriented multi-scale decision making framework for designing both materials (molecules) and processes for separation, reaction, and reactive separation whenever material choice significantly impacts process performance. The inherent nonlinearity and nonconvexity in CAMPD optimization models, introduced through the property and process models, pose challenges to state-of-the-art solvers. Recently, quantum computing (QC) has shown promise for solving complex optimization problems, especially those involving discrete decisions. This motivates us to explore the potential usage of quantum optimization techniques for solving CAMPD problems. We have developed a technique for directly solving a class of mixed integer nonlinear programs using QC. Our approach represents both continuous and integer design decisions by a set of binary variables through encoding schemes. This transformation allows to reformulate certain types of CAMPD problems into Quadratic Unconstrained Binary Optimization (QUBO) models that can be directly solved using quantum annealing techniques. We illustrate this technique for the selection of optimal ionic liquids (IL) and the configuration of a reactor-separator process network. We also discuss several challenges that are associated with quantum optimization when solving large scale CAMPD problems.
Computer-aided Molecular and Process Design (CAMPD) is an equation-oriented multi-scale decision making framework for designing both materials (molecules) and processes for separation, reaction, and reactive separation whenever material choice significantly impacts process performance. The inherent nonlinearity and nonconvexity in CAMPD optimization models, introduced through the property and process models, pose challenges to state-of-the-art solvers. Recently, quantum computing (QC) has shown promise for solving complex optimization problems, especially those involving discrete decisions. This motivates us to explore the potential usage of quantum optimization techniques for solving CAMPD problems. We have developed a technique for directly solving a class of mixed integer nonlinear programs using QC. Our approach represents both continuous and integer design decisions by a set of binary variables through encoding schemes. This transformation allows to reformulate certain types of CAMPD problems into Quadratic Unconstrained Binary Optimization (QUBO) models that can be directly solved using quantum annealing techniques. We illustrate this technique for the selection of optimal ionic liquids (IL) and the configuration of a reactor-separator process network. We also discuss several challenges that are associated with quantum optimization when solving large scale CAMPD problems.
Conceptual process design is a crucial aspect of chemical engineering that involves process synthesis. Mixed-integer nonlinear programming is a powerful framework for modeling such design problems by combining discrete and continuous variables; however, the combinatorial complexity of discrete choices, coupled with nonlinearities, presents challenging monolithic problems. Using decomposition, discrete subproblems can potentially benefit from Ising solvers, while simulators and nonlinear solvers offer powerful tools for handling nonlinearities. This work aims to: evaluate use of Ising-based solvers for discrete optimization and holistic process optimization through two case studies: an ionic liquid selection and its process design, and a more complex problem of drug manufacturing process optimization. The discrete subproblem is formulated as an integer program or quadratic unconstrained binary optimization and solved using a commercial classical or Ising solvers such as simulated annealing (SA), quantum annealing (QA), and entropy computing (EC) respectively. The commercial classical solver had the shortest runtime, whereas EC took the longest, followed by QA and SA, in reaching feasible and optimal solutions. The heuristics identified all or most feasible solutions in a single run, demonstrating advantages in solution diversity and efficient and broad exploration of the solution space over the classical solver, while the classical solver provides an optimality guarantee and rapid convergence speed. In process design, where insights of alternative designs and cost comparisons are more valuable than an optimal solution, heuristics offer a better-suited decision-making strategy. The comparative analysis highlights the strengths of each method and underscores the potential of this heterogeneous computing approach that leverages different methods to address practical optimization problems.
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary Optimization (QUBO) formulation provides a unifying modeling framework for a broad class of NP-hard problems and is naturally suited to quantum computing and quantum-inspired algorithms. Location science, network design, and logistics represent core application domains of discrete optimization, combining high practical impact with substantial computational challenges. In this work, we develop QUBO formulations for several fundamental problems in these domains, including a nonlinear integer formulation of the Discrete Ordered Median Problem (DOMP). Beyond their modeling relevance, these QUBO formulations serve as representative benchmark problems for assessing quantum algorithms and quantum hardware. We further derive a tight bound for the penalty parameter ensuring equivalence between the QUBO formulation and its underlying integer program. Finally, we conduct a comprehensive computational study using QAOA, WS-QAOA, and classical heuristics for QUBO instances of the p-Median Problem and the Fixed-Charge Facility Location Problem (FCFLP), and introduce two effective warm-start strategies for WS-QAOA based on its linear programming relaxation.
Bioprocess optimization spans multiple scales, from molecular interactions to plant-wide operations, presenting challenges due to nonlinearity, high-dimensionality, and computational intractability. Traditional methods, such as Mixed-Integer Nonlinear Programming (MINLP), often fail to efficiently solve these problems. This work explores Hybrid Quantum-Classical (HQC) algorithms as a promising alternative. By integrating quantum solvers for discrete combinatorial optimization with classical solvers for continuous variable refinement, HQC approaches overcome computational bottlenecks inherent to classical techniques. The application of HQC algorithms enhances efficiency, scalability, and decision-making in bioprocess optimization, particularly in metabolic pathway selection, real-time fermentor control, and plant-wide resource allocation. This perspective outlines the theoretical foundation of HQC methods, their applications across bioprocess scales, and future research directions.
The video (https://youtu.be/qB07ueMVw0w) presents our ongoing work on the optimization of cargo logistics processes with containers using quantum computing, mainly in airplanes and barges, of great international relevance. Combinatorial optimization problems are computationally complex in conventional computing. The origins of Quantum Computing date back to the early 90's. This discipline allows solving problems that in conventional computing are complex [1]. We present a Quantum Computing tool, the QUBO method (Quadratic Unconstrained Binary Optimization) [2], which is suitable for formulating combinatorial optimization problems. QUBO is a recently developed tool, based on Quantum Annealing and is implemented in some current quantum computers. It consists of minimizing outputs of the type xTQx with x being a binary decision vector and Q a square or triangular matrix with constant parameters provided by the model. Restrictions can be added to the treated system. These problems have to do with making good decisions in environments where a large number of binary decisions (Yes/No) must be made and each set of decisions produces a corresponding objective function value, such as a cost or benefit value. In the video we also present the example of the Number Partitioning Problem.
Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks.
We propose a unified approach for reformulating diverse computational challenges into Quadratic Unconstrained Binary Optimization (QUBO) models and solving them via quantum annealing. By applying this framework across multiple domains, we demonstrate its flexibility in handling structurally different problems within a single mathematical formulation. The study highlights QUBO’s capability to exploit quantum parallelism, integrate regularization seamlessly, and address ill-posed inverse problems. These advantages position QUBO-based quantum annealing as a promising tool for large-scale optimization and reconstruction tasks, with strong potential for impact in scientific computing, engineering, and data-driven applications.