Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2504.06458

A Framework for Solving Continuous Energy and Power System Problems using Adiabatic Quantum Computing

Zeynab Kaseb, Matthias Möller, Peter Pálenský, Pedro P. Vergara

Published Apr 8, 2025• 0 citations
arXivHTMLPDF

Abstract

The increasing scale and nonlinearity of modern energy and power system problems pose significant challenges to classical numerical solvers. In parallel, advances in quantum and quantum-inspired hardware are expected to improve scalability and offer performance advantages for large-scale optimization problems. Therefore, we propose a novel combinatorial optimization framework that reformulates continuous energy and power system problems into a format executable on quantum/digital annealers. The proposed framework accommodates both real and complex numbers and can represent both linear and nonlinear equations. As a proof of concept, we demonstrate its use in three applications: (i) 2D steady conductive heat transfer for a plate with constant temperature at each edge, where coefficient and boundary condition matrices are developed to solve linear system of equations, (ii) power system parameter identification, where the admittance matrix is estimated given voltage and current measurements, and (iii) power flow analysis, which solves the governing equations for active and reactive power balance. As a proof of concept, the applications are run on small test cases. The results show that the framework effectively and efficiently addresses the three applications and therefore suggest its potential to solve a wide range of energy and power system problems.

DOI
10.48550/arxiv.2504.06458

Related papers

Power flow analysis using quantum and digital annealers: a discrete combinatorial optimization approach

Zeynab Kaseb, Matthias Möller, Pedro P. Vergara +1 more

Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave's Advantage™ quantum annealer, Fujitsu's digital annealer V3, D-Wave's quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.

Scientific Reports•Oct 5, 2024•11 citations

Power flow and optimal power flow using quantum and digital annealers: a computational scalability analysis

Zeynab Kaseb, Matthias Möller, Pedro P. Vergara +1 more

This study further explores reformulating power flow (PF) analysis as a discrete combinatorial optimization problem, proposed in our earlier study using the Adiabatic Quantum Power Flow (AQPF) algorithm, which can be executed on Ising machines, including quantum and quantum-inspired hardware. This approach provides a new representation of the underlying equations, analogous to how neural networks approximate complex functions using simple operations. While the resulting combinatorial optimization problem is NP-hard, it is compatible with emerging quantum hardware designed to address such complexity. We introduce the Adiabatic Quantum Optimal Power Flow (AQOPF) algorithm, which transforms the classical optimal power flow (OPF) equations into quadratic unconstrained binary optimization (QUBO) models. Furthermore, the AQPF and AQOPF algorithms are evaluated on standard test cases ranging from 4- to 1354-bus systems using D-Wave's Advantage\texttrademark\ system (QA), its hybrid quantum-classical solver (HA), and Fujitsu's third-generation Digital Annealer (DAv3) and Quantum-Inspired Integrated Optimization (QIIO) platform. Both full and partitioned formulations are investigated, with particular attention to scalability and robustness in ill-conditioned scenarios. The results demonstrate that the algorithms can reproduce feasible PF and OPF solutions and exhibit promising computational scalability when supported by scalable hardware.

arXiv:2505.15978•May 21, 2025•1 citation

Application of Adiabatic Quantum Computing in Power Grid Optimization

Halina Grzelakowa, Felicja Oliwia Konopka

In addressing the complexity and real-time demands of modern grid optimization in quantum technology, advancements in computing and other fields have provided new avenues for meeting these needs. This article proposes a structured hybrid quantum-classical framework that uses adiabatic quantum computing to plan the operation of large-scale power networks. A large number of experiments were conducted on benchmark power system cases with 14 to 300 nodes, including various topologies and random operating conditions. The aforementioned method first performs preprocessing and problem partitioning. Then, using spatial and temporal partitioning schemes, the most difficult subproblems are assigned to quantum subroutines. The results show that compared to the state-of-the-art traditional algorithms, the hybrid method has a constraint violation rate of less than 0.03 in all test cases, an average operational cost reduction of 6%, and energy savings of 18%. Runtime evaluation shows that the hybrid solver outperforms pure classical and purely quantum methods, and the computation time exhibits sublinear scaling as the grid size increases. The structure can be flexibly adjusted and can still function normally in emergencies, even if parameters and resources are modified or the topology changes. Research indicates that combining adiabatic quantum computing with hybrid optimization systems can enhance the system's scalability, solution quality, and computational efficiency. This method is currently being applied to the construction of new smart grids.

Journal of Applied Automation Technologies•Sep 9, 2025•0 citations

Quantum Hardware-in-the-Loop for Optimal Power Flow in Renewable-Integrated Power Systems

Zeynab Kaseb, Rahul Rane, Aleksandra Lekić +4 more

Quantum computing has emerged as a promising computational paradigm to address unresolved challenges in the modeling and control of modern power systems. However, most existing studies focus on offline simulations, and a practical framework for validating quantum algorithms in real-time operational environments remains lacking. This study proposes a quantum hardware-in-the-loop framework that integrates a real-time digital simulator with quantum and quantum-inspired hardware to solve combinatorial power flow and optimal power flow formulations under dynamic operating conditions. The proposed framework is validated using the IEEE 9- bus test system and a modified version with integrated solar and wind farms. The results confirm successful integration and convergence within a predefined tolerance. The study also identifies key limitations and challenges, such as limited access to quantum and digital annealers and current scalability limitations, that must be considered in future developments. Nevertheless, the results highlight the potential of quantum computing to significantly enhance the modeling and control of future power systems with high penetration of renewable energy sources.

arXiv:2505.13356•IEEE Transactions on Power Systems•May 25, 2026•0 citations

Performance Comparison of Gate-Based and Adiabatic Quantum Computing for AC Power Flow Problem

Zeynab Kaseb, Matthias Möller, Peter Pálenský +1 more

We present the first direct comparison between gate-based quantum computing (GQC) and adiabatic quantum computing (AQC) paradigms for solving the AC power flow (PF) equations. The PF problem is reformulated as a combinatorial optimization problem. For the GQC approach, the Quantum Approximate Optimization Algorithm (QAOA) is employed, while for the AQC approach, the problem is formulated as an Ising model. Numerical experiments on a 4-bus test system evaluate solution accuracy and computational performance. Results obtained using QAOA are benchmarked against those produced by D-Wave's Advantage system and Fujitsu's latest-generation Digital Annealer, implemented through the Quantum-Inspired Integrated Optimization (QIIO) software. The findings provide quantitative insights into the performance trade-offs, scalability, and practical viability of GQC and AQC paradigms for PF analysis, highlighting the potential of quantum optimization algorithms to address the computational challenges associated with the operation of modern electricity grids in the fault-tolerant era.

arXiv:2510.13378•Oct 15, 2025•0 citations

Annealing-Based Quantum Computing for Combinatorial Optimal Power Flow

Thomas Morstyn

This paper proposes the use of annealing-based quantum computing for solving combinatorial optimal power flow problems. Quantum annealers provide a physical computing platform which utilises quantum phase transitions to solve specific classes of combinatorial problems. These devices have seen rapid increases in scale and performance, and are now approaching the point where they could be valuable for industrial applications. This paper shows how an optimal power flow problem incorporating linear multiphase network modelling, discrete sources of energy flexibility, renewable generation placement/sizing and network upgrade decisions can be formulated as a quadratic unconstrained binary optimisation problem, which can be solved by quantum annealing. Case studies with these components integrated with the IEEE European Low Voltage Test Feeder are implemented using D-Wave Systems’ 5,760 qubit Advantage quantum processing unit and hybrid quantum-classical solver.

IEEE Transactions on Smart Grid•Aug 22, 2022•75 citations
The increasing scale and nonlinearity of modern energy and power system problems pose significant challenges to classical numerical solvers. In parallel, advances in quantum and quantum-inspired hardware are expected to improve scalability and offer performance advantages for large-scale optimization problems. Therefore, we propose a novel combinatorial optimization framework that reformulates continuous energy and power system problems into a format executable on quantum/digital annealers. The proposed framework accommodates both real and complex numbers and can represent both linear and nonlinear equations. As a proof of concept, we demonstrate its use in three applications: (i) 2D steady conductive heat transfer for a plate with constant temperature at each edge, where coefficient and boundary condition matrices are developed to solve linear system of equations, (ii) power system parameter identification, where the admittance matrix is estimated given voltage and current measurements, and (iii) power flow analysis, which solves the governing equations for active and reactive power balance. As a proof of concept, the applications are run on small test cases. The results show that the framework effectively and efficiently addresses the three applications and therefore suggest its potential to solve a wide range of energy and power system problems.
Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave's Advantage™ quantum annealer, Fujitsu's digital annealer V3, D-Wave's quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.
This study further explores reformulating power flow (PF) analysis as a discrete combinatorial optimization problem, proposed in our earlier study using the Adiabatic Quantum Power Flow (AQPF) algorithm, which can be executed on Ising machines, including quantum and quantum-inspired hardware. This approach provides a new representation of the underlying equations, analogous to how neural networks approximate complex functions using simple operations. While the resulting combinatorial optimization problem is NP-hard, it is compatible with emerging quantum hardware designed to address such complexity. We introduce the Adiabatic Quantum Optimal Power Flow (AQOPF) algorithm, which transforms the classical optimal power flow (OPF) equations into quadratic unconstrained binary optimization (QUBO) models. Furthermore, the AQPF and AQOPF algorithms are evaluated on standard test cases ranging from 4- to 1354-bus systems using D-Wave's Advantage\texttrademark\ system (QA), its hybrid quantum-classical solver (HA), and Fujitsu's third-generation Digital Annealer (DAv3) and Quantum-Inspired Integrated Optimization (QIIO) platform. Both full and partitioned formulations are investigated, with particular attention to scalability and robustness in ill-conditioned scenarios. The results demonstrate that the algorithms can reproduce feasible PF and OPF solutions and exhibit promising computational scalability when supported by scalable hardware.
In addressing the complexity and real-time demands of modern grid optimization in quantum technology, advancements in computing and other fields have provided new avenues for meeting these needs. This article proposes a structured hybrid quantum-classical framework that uses adiabatic quantum computing to plan the operation of large-scale power networks. A large number of experiments were conducted on benchmark power system cases with 14 to 300 nodes, including various topologies and random operating conditions. The aforementioned method first performs preprocessing and problem partitioning. Then, using spatial and temporal partitioning schemes, the most difficult subproblems are assigned to quantum subroutines. The results show that compared to the state-of-the-art traditional algorithms, the hybrid method has a constraint violation rate of less than 0.03 in all test cases, an average operational cost reduction of 6%, and energy savings of 18%. Runtime evaluation shows that the hybrid solver outperforms pure classical and purely quantum methods, and the computation time exhibits sublinear scaling as the grid size increases. The structure can be flexibly adjusted and can still function normally in emergencies, even if parameters and resources are modified or the topology changes. Research indicates that combining adiabatic quantum computing with hybrid optimization systems can enhance the system's scalability, solution quality, and computational efficiency. This method is currently being applied to the construction of new smart grids.
Quantum computing has emerged as a promising computational paradigm to address unresolved challenges in the modeling and control of modern power systems. However, most existing studies focus on offline simulations, and a practical framework for validating quantum algorithms in real-time operational environments remains lacking. This study proposes a quantum hardware-in-the-loop framework that integrates a real-time digital simulator with quantum and quantum-inspired hardware to solve combinatorial power flow and optimal power flow formulations under dynamic operating conditions. The proposed framework is validated using the IEEE 9- bus test system and a modified version with integrated solar and wind farms. The results confirm successful integration and convergence within a predefined tolerance. The study also identifies key limitations and challenges, such as limited access to quantum and digital annealers and current scalability limitations, that must be considered in future developments. Nevertheless, the results highlight the potential of quantum computing to significantly enhance the modeling and control of future power systems with high penetration of renewable energy sources.
We present the first direct comparison between gate-based quantum computing (GQC) and adiabatic quantum computing (AQC) paradigms for solving the AC power flow (PF) equations. The PF problem is reformulated as a combinatorial optimization problem. For the GQC approach, the Quantum Approximate Optimization Algorithm (QAOA) is employed, while for the AQC approach, the problem is formulated as an Ising model. Numerical experiments on a 4-bus test system evaluate solution accuracy and computational performance. Results obtained using QAOA are benchmarked against those produced by D-Wave's Advantage system and Fujitsu's latest-generation Digital Annealer, implemented through the Quantum-Inspired Integrated Optimization (QIIO) software. The findings provide quantitative insights into the performance trade-offs, scalability, and practical viability of GQC and AQC paradigms for PF analysis, highlighting the potential of quantum optimization algorithms to address the computational challenges associated with the operation of modern electricity grids in the fault-tolerant era.
This paper proposes the use of annealing-based quantum computing for solving combinatorial optimal power flow problems. Quantum annealers provide a physical computing platform which utilises quantum phase transitions to solve specific classes of combinatorial problems. These devices have seen rapid increases in scale and performance, and are now approaching the point where they could be valuable for industrial applications. This paper shows how an optimal power flow problem incorporating linear multiphase network modelling, discrete sources of energy flexibility, renewable generation placement/sizing and network upgrade decisions can be formulated as a quadratic unconstrained binary optimisation problem, which can be solved by quantum annealing. Case studies with these components integrated with the IEEE European Low Voltage Test Feeder are implemented using D-Wave Systems’ 5,760 qubit Advantage quantum processing unit and hybrid quantum-classical solver.