Alternative Current Optimal Power Flow (AC-OPF) is essential for efficient power system planning and real-time operation but remains an NP-hard and non-convex optimization problem with significant computational challenges. This paper proposes a novel hybrid classical-quantum deep learning framework for AC-OPF problem, integrating parameterized quantum circuits (PQCs) for feature extraction with classical deep learning for data encoding and decoding. The proposed framework integrates two types of residual connection structures to mitigate the ``barren plateau" problem in quantum circuits, enhancing training stability and convergence. Furthermore, a physics-informed neural network (PINN) module is incorporated to guarantee tolerable constraint violation, improving the physical consistency and reliability of AC-OPF solutions. Experimental evaluations on multiple IEEE test systems demonstrate that the proposed approach achieves superior accuracy, generalization, and robustness to quantum noise while requiring minimal quantum resources.
Alternative Current Optimal Power Flow (AC-OPF) is essential for efficient power system planning and real-time operation but remains an NP-hard and non-convex optimization problem with significant computational challenges. This paper proposes a novel hybrid classical-quantum deep learning framework for AC-OPF problem, integrating parameterized quantum circuits (PQCs) for feature extraction with classical deep learning for data encoding and decoding. The proposed framework integrates two types of residual connection structures to mitigate the ``barren plateau" problem in quantum circuits, enhancing training stability and convergence. Furthermore, a physics-informed neural network (PINN) module is incorporated to guarantee tolerable constraint violation, improving the physical consistency and reliability of AC-OPF solutions. Experimental evaluations on multiple IEEE test systems demonstrate that the proposed approach achieves superior accuracy, generalization, and robustness to quantum noise while requiring minimal quantum resources.
Quantum computing provides alternative algorithmic approaches to solve computationally challenging problems and has shown potential advantages compared to classical methods for specific problem classes. This thesis explores variational quantum algorithms (VQAs) for solving the alternating current optimal power flow (AC OPF) problem and the AC power flow (PF) problem. Both tasks are fundamental to power system analysis, operation, and planning, but they become increasingly challenging as grid size and complexity grow. The first main contribution of the thesis introduces a variational quantum framework for solving the OPF problem, formulated as a nonconvex quadratically constrained quadratic program. The proposed method encodes primal and dual optimization variables using two parameterized quantum circuits (PQCs), allowing the OPF Lagrangian to be expressed as expectations over quantum observables. An OPF solution can be found by minimizing the Lagrangian over the parameters of the first PQC and maximizing it over the parameters of the second PQC. The proposed framework seeks saddle points of the Lagrangian in a hybrid fashion. The gradients of the Lagrangian are estimated using the two PQCs, and PQC parameters are updated classically using a primal-dual method. A key innovation is to permute the primal variables of the original problem, so the corresponding quantum observables adhere to a banded form that facilitates a novel qubit-efficient quantum measurement protocol. The second main contribution presents a quantum machine learning (QML) approach for learning AC PF solutions using a data-embedded PQC. The method first poses a single PF instance as a nonlinear least-squares problem over PQC parameters. Second, the PF specifications are embedded as features into another PQC, and the resultant QML model is trained to learn the PF mapping. Once presented with a new problem instance, the trained QML model can perform the prediction step efficiently in real-time operation. Third, a novel protocol is devised to efficiently measure PF observables by leveraging the graph structure of a power network. The proposed quantum AC PF/OPF framework sets the foundations for addressing more elaborate grid tasks via quantum computing. More broadly, the proposed quantum paradigms can be used to achieve safe QML as PQCs are trained to comply with data-dependent constraints.
Optimal Power Flow (OPF) is a fundamental optimisation problem in power systems, aiming to minimize the generation cost dispatch while satisfying operational constraints. Traditional optimisation methods, especially the AC-OPF formulation, struggle to converge or find optimal solutions due tothenon-linear andnon-convexnatureoftheproblem. Thisstudyaddressesthe AC-OPF using a hybrid iterative algorithm that combines classical and quantum computing, where Quantum Annealing assists in optimizing decision variables. ThemethodologysplitstheAC-OPFintotwointerrelatedproblems. Thefirstsub-problemisthe classical OPFformulation, whichincorporatesallelectricalnetworkcomponentsandminimizes the objective function under technical and operational constraints. The second sub-problem, also known as the master problem, is a binary problem that assumes activation states of the generators, while minimizingcostsofgenerationandstart-upcostsfordifferenttimesteps. This forms aBinary Integer Linear Programming (BILP) problem, which is well-suited for quantum computing due to its discrete structure and combinatorial complexity. Once the BILP is defined, it is converted into a Hamiltonian and evolved using Quantum Annealing throughtheQiboframework. Theresultingoptimalbinarycombinationisthenapplied to the network model and solved classically. If the solution is feasible and optimal, the process ends. If not, the combination is excluded from the BILP and added as a constraint to guide the search for the next best feasible solution. This methodology is tested on two IEEE networks of 9 to evaluate computational speedup and assess the limitations of actual quantum hardware. Once this is done, future work will explore the use of Quantum Machine Learning to generate 24-hour load and generation profiles, while in this work, an LSTM is used, enabling the AC-OPF solutions.
Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.
With increasing prevalence of distributed energy resources (DERs), the growing threat of cyber-physical attacks, and the need for real-time optimization present major challenges for modern smart grids. With challenges also come opportunities. Although classical machine learning (ML) models, such as deep neural networks (DNNs), have shown promise toward meeting some of these challenges, they often struggle with the computational complexity when vast volumes of grid data are involved. The problems are particularly acute in situations when real-time responses are essential. This paper proposes a framework that integrates classical and quantum neural networks (QNNs) to initiate a new paradigm of time-sensitive grid management. We explore the potential of quantum computing to enhance the capabilities of classical neural networks in two critical applications: (1) real-time anomaly detection for cybersecurity and (2) dynamic optimal power flow (OPF) management for grid stability. We propose a hybrid quantum-classical neural network framework suitable for near-term quantum devices, discuss the theoretical advantages in computational speed and model capacity, and address the significant challenges related to quantum hardware noise, algorithmic design, and data encoding. The framework is flexible enough to allow for futureproofing as QNNs and quantum computing hardware continue to evolve. Our analysis suggests that QNNs, even in their current nascent stage, hold great promise to revolutionize smart grid analytics by solving complex, time-sensitive classification and optimization problems that are currently difficult or intractable for classical methods. The study therefore lays the groundwork for a future smart grid that is more secure, efficient, and robust.
In this work, we introduce the Quantum-Classical Hybrid Physics-Informed Neural Network with Multiplicative and Additive Couplings (QPINN-MAC): a novel hybrid architecture that integrates the framework of Physics-Informed Neural Networks (PINNs) with that of Quantum Neural Networks (QNNs). Specifically, we prove that through strategic couplings between classical and quantum components, the QPINN-MAC retains the universal approximation property, ensuring its theoretical capacity to represent complex solutions of ordinary differential equations (ODEs). Simultaneously, we demonstrate that the hybrid QPINN-MAC architecture actively mitigates the barren plateau problem, regions in parameter space where cost-function gradients decay exponentially with circuit depth, a fundamental obstacle in QNNs that hinders optimization during training. Furthermore, we prove that these couplings prevent gradient collapse, ensuring trainability even in high-dimensional regimes. Thus, our results establish a new pathway for constructing quantum-classical hybrid models with theoretical convergence guarantees, which are essential for the practical application of QPINNs.
This study introduces a quantum-accelerated framework that integrates quantum optimization with physics-informed neural networks (PINNs) to solve PDEs more efficiently. By leveraging the Quantum Approximate Optimization Algorithm (QAOA), the proposed framework enhances the initialization and boundary parameter optimization of PINNs, addressing key challenges such as slow convergence and high computational cost. The hybrid approach combines the data efficiency and physical constraint embedding capabilities of PINNs with the computational advantages of quantum optimization, enabling faster and more accurate solutions for complex PDEs. The framework was validated using the Shuhao Cao PDE dataset, demonstrating significant improvements in training efficiency and accuracy compared to traditional numerical solvers and classical PINNs. Experimental results highlight that quantum optimization effectively accelerates convergence by optimizing initial conditions and boundary constraints, reducing the computational overhead associated with classical training processes. Despite its reliance on emerging quantum hardware and the sensitivity of PINNs to hyperparameter selection, this approach offers a scalable and robust solution for solving high-dimensional PDEs. The findings underscore the potential of hybrid quantum-classical methods in advancing scientific computing, providing a foundation for future research in stochastic PDEs, multi-physics problems, and other real-world applications.