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.
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.
Interconnection studies require solving numerous instances of the AC load or power flow (AC PF) problem to simulate diverse scenarios as power systems navigate the ongoing energy transition. To expedite such studies, this work leverages recent advances in quantum computing to find or predict AC PF solutions using a variational quantum circuit (VQC). VQCs are trainable models that run on modern-day noisy intermediate-scale quantum (NISQ) hardware to accomplish elaborate optimization and machine learning (ML) tasks. Our first contribution is to pose a single instance of the AC PF as a nonlinear least-squares fit over the VQC trainable parameters (weights) and solve it using a hybrid classical/quantum computing approach. The second contribution is to feed PF specifications as features into a data-embedded VQC and train the resultant quantum ML (QML) model to predict general PF solutions. The third contribution is to develop a novel protocol to efficiently measure AC-PF quantum observables by exploiting the graph structure of a power network. Preliminary numerical tests indicate that the proposed VQC models attain enhanced prediction performance over a deep neural network despite using much fewer weights. The proposed quantum AC-PF framework sets the foundations for addressing more elaborate grid tasks via quantum computing.
Conic programs arising in physics, quantum information, machine learning, and engineering are often defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers, the computational complexity scales unfavorably with graph size. We propose a variational quantum paradigm for solving conic programs, including quadratically constrained quadratic programs and semidefinite programs. We encode primal variables via the state of a parameterized quantum circuit (PQC) and dual variables via the probability mass function associated with a second PQC. The Lagrangian function can thus be expressed as scaled expectations of quantum observables. We pursue approximately stationary points of the Lagrangian by minimizing/maximizing the Lagrangian over the parameters of the first/second PQC. This is accomplished in a hybrid fashion: gradients are estimated using the two PQCs, while their parameters are updated classically using a primal-dual method. We propose permuting primal variables so that related observables have a banded form, enabling efficient measurement. We provide a complexity analysis that is useful to determine which problem types may enjoy quantum advantage. The framework is applied to the AC OPF problem, a large-scale optimization problem central to electric power system operation. Numerical tests on the IEEE 57-node system using PennyLane's simulator show that the proposed doubly variational quantum framework can find high-quality OPF solutions. While this demonstration does not yield a quantum speedup, the results serve as a proof-of-concept and highlight challenges toward practical quantum advantage. Although showcased for OPF, the framework has broader scope, including conic programs with many variables and constraints, problems defined over sparse graphs, and training quantum machine learning models to satisfy constraints.
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.
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.
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.
This paper addresses the critical challenge of Op-timal Power Flow (OPF) in electrical engineering, emphasizing the intersection of complexity and technological advancements. Leveraging quantum computation, particularly the Primal-Dual Interior Point Method (PD-IPM) and the Harrow-Hassidim-Lloyd (HHL) algorithm, we explore enhanced solutions for both Alternating Current OPF (ACOPF) and Direct Current OPF (DCOPF). PD-IPM generates linear systems during optimization, aligning with the selected quantum techniques that offer expo-nential speedup. We investigate the scalability and challenges of HHL, emphasizing the current limitations for larger power systems. Additionally, we introduce a hybrid approach that dynamically transitions between quantum and classical methods to optimize convergence. Our study evaluates the proposed methodology's performance under diverse error conditions, em-phasizing its potential to revolutionize solving times for OPF in power systems.