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Integrating quantum computing into building-to-grid control framework: Application of benders decomposition in mixed-integer nonlinear programming

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BUILDING SIMULATION 2025年 1-16页

作者： Deng, Zhipeng Wang, Xuezheng Dong, Bing Univ Cent Florida Coll Engn & Comp Sci Dept Mech & Aerosp Engn Orlando FL USA Syracuse Univ Dept Mech & Aerosp Engn Syracuse NY 13244 USA

Buildings use a large amount of energy in the United States. It is important to optimally manage and coordinate the resources across building and power distribution networks to improve overall efficiency. Optimizing the power grid with discrete variables was very challenging for traditional computers and algorithms, as it is an NP-hard problem. In this study, we developed a new optimization solution based on quantum computing for BTG integration. We first used MPC for building loads connected with a commercial distribution grid for cost reduction. Then we used discretization and Benders Decomposition methods to reformulate the problem and decompose the continuous and discrete variables, respectively. We used D-Wave quantum computer to solve dual problems and used conventional algorithm for primal problems. We applied the proposed method to an IEEE 9-bus network with 3 commercial buildings and over 300 residential buildings to evaluate the feasibility and effectiveness. Compared with traditional optimization methods, we obtained similar solutions with some fluctuations and improved computational speed from hours to seconds. The time of quantum computing was greatly reduced to less than 1% of traditional optimization algorithm and software such as MATLAB. Quantum computing has proved the potential to solve large-scale discrete optimization problems for urban energy systems.

关键词： smart grid model predictive control IEEE 9-bus quadratic unconstrained binary optimization quantum annealing

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Combinatorial optimization with quantum computers

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ENGINEERING optimization 2025年第1期57卷 208-233页

作者： Chicano, Francisco Luque, Gabiel Dahi, Zakaria Abdelmoiz Gil-Merino, Rodrigo Univ Malaga ITIS Software Malaga Spain Univ Lille BONUS Res Team CNRS Inria Lille France Int Univ Rioja UNIR Sch Engn & Technol Logrono Spain

Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. Though a single classical computer transforms one particular binary input into an output after applying one operator to the input, a quantum computer can apply the operator to a superposition of binary strings to provide a superposition of binary outputs, performing computations apparently in parallel. This feature allows quantum computers to speed up the computation compared to classical algorithms. Unsurprisingly, quantum algorithms have been proposed to solve optimization problems in quantum computers. Furthermore, a family of quantum machines called quantum annealers is specially designed to solve optimization problems. This article provides an introduction to quantum optimization from a practical point of view. It introduces the reader to the use of quantum annealers and quantum gate-based machines to solve optimization problems.

关键词： Quantum optimization quantum computing quantum annealer quadratic unconstrained binary optimization

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Calculating Nash equilibrium on quantum annealers

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ANNALS OF OPERATIONS RESEARCH 2025年第2期346卷 1109-1126页

作者： Khan, Faisal Shah Okrut, Olga Cannon, Keith El-Safty, Kareem H. Elsokkary, Nada Dark Star Quantum Lab Apex NC 27526 USA Khalifa Univ Ctr Cyber Phys Syst Abu Dhabi U Arab Emirates

Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. To solve a problem using quantum annealing, the problem requires formatting as a discrete quadratic function without constraints. The problem of finding Nash equilibrium in two-player, non-cooperative games is a two-fold quadratic optimization problem with constraints. This problem was formatted as a single, constrained quadratic optimization in 1964 by Mangasarian and Stone. Here, we show that adding penalty terms to the quadratic function formulation of Nash equilibrium gives a quadratic unconstrained binary optimization (QUBO) formulation of this problem that can be executed on quantum annealers. Three examples are discussed to highlight the success of the formulation, and an overall, time-to-solution (hardware + software processing) speed up by seven to ten times is reported on quantum annealers developed by D-Wave System.

关键词： Nash equilibrium Quantum annealing Quantum computing quadratic unconstrained binary optimization Adiabatic quantum computing

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Improved Posiform Planting Algorithm for Random Generation of binary optimization Problems

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SN Computer Science 2025年第5期6卷 1-16页

作者： Isermann, Stefan Essen 45259 Germany

Logical planted quadratic unconstrained binary optimization problems (QUBO) are artificial problems for benchmarking different Ising machines and optimization algorithms. In particular, they are suitable for investigating whether quantum annealers have an advantage over classical methods. In a recently published paper, an algorithm called posiform planting is proposed that enables a new class of logically planted QUBOs. These have a unique minimum for an arbitrary configuration and are generated via a randomly generated 2-satisfiability (2-SAT) problem. Moreover, these can also be created for sparsely connected architectures of current quantum annealers. By analyzing the phase transition from many to a unique solution of a 2-SAT problem, which is qualitatively different from the phase transition of a 2-SAT problem from satisfiable to unsatisfiable, we show that this algorithm has time complexity O(nlogn), where n is the number of binary variables of the QUBO. In addition, a large number of random 2-SAT clauses are required to ensure the uniqueness of the global minimum, which leads to the easy solvability of the QUBOs. Instead, we describe an algorithm of O(n) that requires fewer clauses and generates random QUBOs that are more difficult to solve and are therefore better suited for benchmarking. © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2025.

关键词： 2-SAT 2-SAT phase transition Graph theory Ising machines quadratic unconstrained binary optimization Quantum annealing QUBO

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The quantum Ising model for perfect matching and solving it with variational quantum eigensolver

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Science China(Information Sciences) 2024年第9期67卷 306-320页

作者： Qilin ZHENG Pingyu ZHU Chao WU Miaomiao YU Weihong LUO Ping XU Institute for Quantum Information and State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Hefei National Laboratory

Obtaining all perfect matchings of a graph is a tough problem in graph theory, and its complexity belongs to the #P-Complete class. The problem is closely related to combinatorics, marriage matching problems, dense subgraphs, the Gaussian boson sampling, chemical molecular structures, and dimer *** this paper, we propose a quadratic unconstrained binary optimization formula of the perfect matching problem and translate it into the quantum Ising model. We can obtain all perfect matchings by mapping them to the ground state of the quantum Ising Hamiltonian and solving it with the variational quantum eigensolver. Adjusting the model's parameters can also achieve the maximum or minimum weighted perfect matching. The experimental results on a superconducting quantum computer of the Origin Quantum Computing Technology Company show that our model can encode 2~n dimensional optimization space with only O（n） qubits consumption and achieve a high success probability of the ground state corresponding to all perfect matchings. In addition, the further simulation results show that the model can support a scale of more than 14 qubits, effectively resist the adverse effects of noise, and obtain a high success probability at a shallow variational depth. This method can be extended to other combinatorial optimization problems.

关键词： perfect matching Ising model quantum Hamiltonian variational quantum eigensolver quadratic unconstrained binary optimization

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Quantum Approximate optimization Algorithm applied to multi-objective routing for large scale 6G networks

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Computer Networks 2025年 267卷

作者： Bouchmal, Oumayma Cimoli, Bruno Stabile, Ripalta Vegas Olmos, Juan Jose Tafur Monroy, Idelfonso Department of Electrical Engineering Eindhoven University of Technology Eindhoven Netherlands Software Architecture NVIDIA Corporation Yokneam Israel

A multi-objective optimization problem involves optimizing two or more conflicting objectives simultaneously. This type of problem arises in many scientific and industrial areas and it is classified as NP-Hard. Network routing optimization with multiple objectives falls into this category. In the context of 6G networks, solving this problem will become even more challenging due to the exponential growth of Internet of Things devices and the high quality of service requirements. Finding good quality solutions for large-scale networks will be increasingly difficult. In this paper, we introduce a quantum-inspired routing optimization scheme in which noisy-intermediate scale quantum computers (NISQ) can be used to solve the Multi-Objective Routing Problem (MORP). We evaluate the application of the proposed scheme in detail by first developing the mathematical formulas for both single-objective and multi-objective routing and mapping the problem onto gate-based models by using the quadratic unconstrained binary optimization (QUBO) approach. To validate the proposed scheme, we use the quantum approximate optimization algorithm (QAOA), the go-to approach for solving combinatorial optimization problems that are classically intractable. For the simulation, we use the IBM-Qasm simulator and Qiskit framework. Additionally, we use the Chernoff Bound as a standard technique to estimate the sample complexity of QAOA. Finally, we provide a detailed numerical and theoretical analysis of the proposed scheme, including its time complexity, resource requirements, and the challenges associated with it. Our results demonstrate that the proposed approach operates with a time complexity of O(E2) per iteration in both single and multi-objective scenarios, with an overall runtime of (niteration + nCB) ⋅ O(E2) influenced by the sampling overhead, significantly outperforming Dijkstra's algorithm in the multi-objective case, where the complexity increases to O(2k(N(k+logN)+2kE)). © 2025 The Au

关键词： 6G Multi-objective routing quadratic unconstrained binary optimization Quantum Approximate optimization Algorithm Quantum computing Quantum optimization

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Mapping a logical representation of TSP to quantum annealing

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QUANTUM INFORMATION PROCESSING 2021年第12期20卷 1-21页

作者： Silva, Carla Aguiar, Ana Lima, Priscila M., V Dutra, Ines Univ Porto Fac Sci Dept Comp Sci Porto Portugal Univ Porto Fac Engn Inst Telecomunicacoes Porto Portugal Univ Porto Fac Engn Dept Elect & Comp Engn Porto Portugal Univ Fed Rio de Janeiro PESC COPPE CT Rio De Janeiro Brazil Univ Fed Rio de Janeiro Tercio Pacitti Inst CCMN Rio De Janeiro Brazil Univ Porto Fac Sci CINTESIS Porto Portugal

This work presents the mapping of the traveling salesperson problem (TSP) based in pseudo-Boolean constraints to a graph of the D-Wave Systems Inc. We first formulate the problem as a set of constraints represented in propositional logic and then resort to the SATyrus approach to convert the set of constraints to an energy minimization problem. Next, we transform the formulation to a quadratic unconstrained binary optimization problem (QUBO) and solve the problem using different approaches: (a) classical QUBO using simulated annealing in a von Neumann machine, (b) QUBO in a simulated quantum environment, (c) QUBO using the D-Wave quantum machine. Moreover, we study the amount of time and execution time reduction we can achieve by exploring approximate solutions using the three approaches. Results show that for every graph size tested with the number of nodes less than or equal to 7, we can always obtain at least one optimal solution. In addition, the D-Wave machine can find optimal solutions more often than its classical counterpart for the same number of iterations and number of repetitions. Execution times, however, can be some orders of magnitude higher than the classical or simulated approaches for small graphs. For a higher number of nodes, the average execution time to find the first optimal solution in the quantum machine is 26% (n = 6) and 47% (n = 7) better than the classical.

关键词： Adiabatic quantum computation quadratic unconstrained binary optimization Constraint and logic programming Applications Pseudo-Boolean optimization

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A conflict clique mitigation method for large-scale satellite mission planning based on heterogeneous graph learning

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ADVANCED ENGINEERING INFORMATICS 2024年 62卷

作者： Feng, Xiaoen Xu, Minqiang Li, Yuqing Harbin Inst Technol Deep Space Explorat Res Ctr Harbin 150001 Peoples R China

For the large-scale and intensive demands of satellite remote sensing observation, the complexity of constraint relationships grows explosively with expansion of satellite task scale. How to efficiently deal with the complex and temporal varying constraint conflicts, and mine the implicit knowledge existing among satellite mission constraints, which is significant to enhance scheduling efficiency, however, is also a core difficulty in the satellite scheduling problem. In this paper, we propose a conflict clique mitigation method based on dynamic taskconstrained heterogeneous graph learning to solve large-scale satellite mission scheduling. The method exploits the advantage of heterogeneous graphs to characterize multiple unstructured relationships, and projects the temporal-varying features of constraint conflicts to the spatial topology of multiple nodes and edges in a heterogeneous graph. Thus, a dynamic constraints heterogeneous graph model for satellite tasks based on sampling critical conflict cliques is developed. And an improved heterogeneous attention network with quadratic unconstrained binary optimization (HAN-QUBO) is proposed, which is able to deal with the heterogeneous graphs and attempts to represent the implicit principles of multiple constraints of satellite missions, so that the valuable strategies and experiences of conflict mitigation can be extracted. The simulation experiments demonstrate that the method can provide effective empirical guidance for multi-satellite scheduling, greatly relieve the pressure of cumbersome constraint conflict checking process for large-scale tasks. The average number of conflict resolutions has been reduced by about 73.48 % for EOSSPs with tens of thousands tasks, while the quality of solutions is maintained at the same time, which significantly improves the efficiency of multisatellite scheduling.

关键词： Earth observation satellite scheduling problem (EOSSP) Large-scale multi-satellite missions Heterogeneous graph Heterogeneous attention network (HAN) quadratic unconstrained binary optimization (QUBO)

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Dynamic optimization on quantum hardware: Feasibility for a process industry use case

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COMPUTERS & CHEMICAL ENGINEERING 2024年 186卷

作者： Nenno, Dennis M. Caspari, Adrian Rhein Westfal TH Aachen Proc Syst Engn AVTSVT D-52074 Aachen Germany

The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model -predictive control, where rapid and reliable computations are critical. Conventional methods can struggle to surmount the complexities of such tasks. Quantum computing and quantum annealing emerge as avant-garde contenders to transcend conventional computational constraints. We convert a dynamic optimization problem, characterized by an optimization problem with a system of differential-algebraic equations embedded, into a quadratic unconstrained binary optimization problem, enabling quantum computational approaches. The empirical findings synthesized from classical methods, simulated annealing, quantum annealing via D-Wave's quantum annealer, and hybrid solver methodologies, illuminate the intricate landscape of computational prowess essential for tackling complex and high -dimensional dynamic optimization problems. Our findings suggest that while quantum annealing is a maturing technology that currently does not outperform state-of-the-art classical solvers, continuous improvements could eventually aid in increasing efficiency within the chemical process industry.

关键词： Quantum computing Quantum annealing Dynamic optimization Process industry Chemical reactor Full discretization quadratic unconstrained binary optimization problem

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Enhancing quantum annealing performance for the molecular similarity problem

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QUANTUM INFORMATION PROCESSING 2017年第5期16卷 1-27页

作者： Hernandez, Maritza Aramon, Maliheh IQB Informat Technol IQBit Vancouver BC V6B 4W4 Canada IQBit Vancouver BC V6B 4W4 Canada

Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to enhance the efficiency of such a solver. In this work, we present a quantum annealing approach to measure similarity among molecular structures. Implementing real-world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity, intrinsic control error, and limited precision. In order to overcome the limited connectivity, a problem must be reformulated using minor-embedding techniques. Using a real data set, we investigate the performance of a quantum annealer in solving the molecular similarity problem. We provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance. Common practices for embedding include minimizing either the number of qubits or the chain length and determining the strength of ferromagnetic couplers empirically. We show that current criteria for selecting an embedding do not improve the hardware's performance for the molecular similarity problem. Furthermore, we use a theoretical approach to determine the strength of ferromagnetic couplers. Such an approach removes the computational burden of the current empirical approaches and also results in hardware solutions that can benefit from simple local classical improvement. Although our results are limited to the problems considered here, they can be generalized to guide future benchmarking studies.

关键词： Quantum annealing Quantum optimization Molecular similarity Minor embedding Parameter setting quadratic unconstrained binary optimization

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