Optimal power flow (OPF) solved by an interior-point method (IPM) requires repeatedly solving Newton linear systems. When variational quantum linear solvers (VQLS) are used, each IPM iteration involves an additional nested inner variational optimization loop, which can significantly slow the overall quantum-assisted IPM convergence. To address this challenge, this paper proposes a dual-level trainable quantum IPM framework for OPF that leverages early solver-generated trajectories rather than relying on single-point prediction. The key observation is that early IPM iterates provide informative primal-dual, slack, and barrier-variable evolution about the path to optimality, while early VQLS parameter updates provide useful information about the later variational search. At the quantum-solver level, a trainable parameter model uses a short prefix of the VQLS parameter trajectory to project the remaining variational search toward a lower-cost region. At the OPF-solver level, a second trainable model uses early primal-dual IPM iterates to project a later central path state, which is restored to an admissible point before IPM refinement continues. Simulation studies show that the proposed approach reduces the number of variational updates by up to $95\%$ while maintaining OPF objective values close to the classical IPM reference. A 2-bus demonstration on real quantum hardware is also included to validate the implementation of the proposed workflow.
Optimal power flow (OPF) solved by an interior-point method (IPM) requires repeatedly solving Newton linear systems. When variational quantum linear solvers (VQLS) are used, each IPM iteration involves an additional nested inner variational optimization loop, which can significantly slow the overall quantum-assisted IPM convergence. To address this challenge, this paper proposes a dual-level trainable quantum IPM framework for OPF that leverages early solver-generated trajectories rather than relying on single-point prediction. The key observation is that early IPM iterates provide informative primal-dual, slack, and barrier-variable evolution about the path to optimality, while early VQLS parameter updates provide useful information about the later variational search. At the quantum-solver level, a trainable parameter model uses a short prefix of the VQLS parameter trajectory to project the remaining variational search toward a lower-cost region. At the OPF-solver level, a second trainable model uses early primal-dual IPM iterates to project a later central path state, which is restored to an admissible point before IPM refinement continues. Simulation studies show that the proposed approach reduces the number of variational updates by up to 95% while maintaining OPF objective values close to the classical IPM reference. A 2-bus demonstration on real quantum hardware is also included to validate the implementation of the proposed workflow.
This paper presents a quantum-enhanced optimization approach for solving optimal power flow (OPF) by integrating the interior point method (IPM) with a coherent variational quantum linear solver (CVQLS). The objective is to explore the applicability of quantum computing to power systems optimization and address the associated challenges. A comparative analysis of state-of-the-art quantum linear solvers—Harrow-Hassidim-Lloyd (HHL), variational quantum linear solver (VQLS), and CVQLS—revealed that CVQLS is most suitable for OPF due to its stability with ill-conditioned matrices, such as the Hessian in IPM. To ensure high-quality solutions, prevent suboptimal convergence, and avoid the barren plateau problem, we propose a quantum circuit parameter initialization technique along with a method to guide the IPM along the central path. Moreover, we design an ansatz tailored for OPF, optimizing the expressibility and trainability of the quantum circuit to ensure efficient convergence and robustness in solving quantum OPF. Various optimizers are also tested for quantum circuit parameter optimization to select the best one. We evaluate our approaches on multiple systems to show their effectiveness in providing reliable OPF solutions. Simulations for the 2-bus system are conducted on a commercial IBMQ quantum device, while simulations for the other larger cases are performed using the IBM quantum simulator. While promising, CVQLS is limited by current quantum hardware, especially for larger systems. We use a quantum noise simulator to test scalability.
This paper presents three quantum interior-point methods (QIPMs) tailored to tackle the DC optimal power flow (DCOPF) problem using noisy intermediate-scale quantum devices. The optimization model is redefined as a linearly constrained quadratic optimization. By incorporating the Harrow-Hassidim-Lloyd (HHL) quantum algorithm into the IPM framework, Newton's direction is determined through the resolution of linear equation systems. To mitigate the impact of HHL error and quantum noise on Newton's direction calculation, we present a noise-tolerant quantum IPM (NT-QIPM) approach. This approach provides high-quality OPF solutions even in scenarios where inexact solutions to the linear equation systems result in approximated Newton's directions. Moreover, to enhance performance in cases of slow convergence and uphold the feasibility of OPF outcomes upon convergence, we propose a hybrid strategy, classically augmented NT-QIPM. This technique is designed to expedite convergence relative to classical IPM while maintaining the solution accuracy. The efficacy of the proposed quantum IPM variants is studied through comprehensive simulations and error analyses on 3-bus, 5-bus, 118-bus, and 300-bus systems, highlighting their potential and promise in addressing challenging OPF scenarios. By modeling the errors and incorporating quantum computer noise, we simulate the proposed algorithms on both Qiskit and classical computers to gain a deeper understanding of the effectiveness and feasibility of our methods under realistic conditions.
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.
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior point methods (IPMs). Despite their favorable polynomial-time convergence, conventional IPMs often suffer from high per-iteration computational costs, especially for dense problem instances. Recent advances in quantum computing, particularly quantum linear system solvers, offer promising avenues to accelerate the most computationally intensive steps of IPMs. However, practical challenges such as quantum error, hardware noise, and sensitivity to poorly conditioned systems remain significant obstacles. In response, a series of Quantum IPMs (QIPMs) has been developed to address these challenges, incorporating techniques such as feasibility maintenance, iterative refinement, and preconditioning. In this work, we review this line of research with a focus on our recent contributions, including an almost-exact QIPM framework. This hybrid quantum-classical approach constructs and solves the Newton system entirely on a quantum computer, while performing solution updates classically. Crucially, all matrix-vector operations are executed on quantum hardware, enabling the method to achieve an optimal worst-case scalability w.r.t dimension, surpassing the scalability of existing classical and quantum IPMs.
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are polynomial-time algorithms with rapid convergence, their per-iteration cost can be prohibitively high for dense large-scale LO problems. Quantum linear system solvers have shown potential in accelerating the solution of linear systems arising in IPMs. In this work, we introduce a novel almost-exact quantum IPM, where the Newton system is constructed and solved on a quantum computer, while solution updates occur on a classical machine. Additionally, all matrix-vector products are performed on the quantum hardware. This hybrid quantum-classical framework achieves an optimal worst-case scaling of O(n2) for fully dense LO problems. To ensure high precision, despite the limited accuracy of quantum operations, we incorporate iterative refinement techniques both within and outside the proposed IPM iterations. The proposed algorithm has a quantum complexity of O(n1.5κAlog(ε1)) queries to QRAM and O(n2log(ε1)) classical arithmetic operations. Our method outperforms the worst-case complexity of prior classical and quantum IPMs, offering a significant improvement in scalability and computational efficiency.
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.