The proliferation of power electronics in multi-terminal transmission grids has increasingly led to harmonic distortions and dynamic instabilities. While Resonance Mode Analysis (RMA) provides deep insights into these system resonances, evaluating the critical modes of large-scale grids presents a severe computational bottleneck. Classical iterative techniques must continuously diagonalize massively high-dimensional, non-Hermitian admittance matrices across a wide frequency spectrum, a process that rapidly exhausts classical memory and processing limits. To overcome this scaling barrier, we propose a novel quantum-classical hybrid methodology that natively maps the transmission grid's admittance matrix onto a Quantum Processing Unit (QPU). Because the grid's matrix is non-Hermitian, standard quantum eigensolvers are insufficient; thus, we employ the Real Variance-based Variational Quantum Eigensolver (RVVQE) algorithm to accurately extract the complex eigenvalues that represent the system's modes. Validated against a standard 5-bus transmission system, the quantum-derived critical-resonance modal impedances demonstrate near-perfect alignment with the exact classical frequency responses. Crucially, by encoding the grid's state logarithmically into quantum memory, this methodology bypasses classical RAM limitations. The successful implementation of the RVVQE framework not only bridges the mathematical topologies of dissipative electrical grids and open quantum systems but also provides a profoundly scalable architecture capable of diagnosing resonance instabilities in massive, continental-scale networks that currently exceed classical computational boundaries.
The proliferation of power electronics in multi-terminal transmission grids has increasingly led to harmonic distortions and dynamic instabilities. While Resonance Mode Analysis (RMA) provides deep insights into these system resonances, evaluating the critical modes of large-scale grids presents a severe computational bottleneck. Classical iterative techniques must continuously diagonalize massively high-dimensional, non-Hermitian admittance matrices across a wide frequency spectrum, a process that rapidly exhausts classical memory and processing limits. To overcome this scaling barrier, we propose a novel quantum-classical hybrid methodology that natively maps the transmission grid's admittance matrix onto a Quantum Processing Unit (QPU). Because the grid's matrix is non-Hermitian, standard quantum eigensolvers are insufficient; thus, we employ the Real Variance-based Variational Quantum Eigensolver (RVVQE) algorithm to accurately extract the complex eigenvalues that represent the system's modes. Validated against a standard 5-bus transmission system, the quantum-derived critical-resonance modal impedances demonstrate near-perfect alignment with the exact classical frequency responses. Crucially, by encoding the grid's state logarithmically into quantum memory, this methodology bypasses classical RAM limitations. The successful implementation of the RVVQE framework not only bridges the mathematical topologies of dissipative electrical grids and open quantum systems but also provides a profoundly scalable architecture capable of diagnosing resonance instabilities in massive, continental-scale networks that currently exceed classical computational boundaries.
Non-Hermitian operators naturally arise in the description of open quantum systems, which exhibit features such as resonances and decay processes, where the associated eigenvalues are complex. Standard quantum algorithms, including the Variational Quantum Eigensolver (VQE), are designed for Hermitian operators and are ineffective in recovering correct eigenvalues for non-Hermitian matrices. We present a systematic formulation based on a Real Variance-based Variational Quantum Eigensolver (RVVQE) for non-Hermitian operators. A correct cost function that guarantees convergence to the true eigenstates is identified. Our implementation utilizes Hermitian measurements only, rendering the algorithm easily deliverable. The performance and scalability of the proposed algorithm on a hierarchy of dense non-Hermitian matrices of increasing dimension are demonstrated with numerical results and computational metrics.
The efficient computation of higher-order modes in multiconductor transmission lines is crucial, as these modes alter the distribution of TEM modes and increase cross-talk, affecting electromagnetic compatibility and signal integrity in high-frequency circuits. Traditional numerical methods face challenges in handling large-scale eigenvalue problems due to increasing computational complexity. Quantum computing offers a promising alternative by leveraging quantum principles such as superposition and entanglement to solve large eigenvalue problems more efficiently than classical solvers. In this work, we explore the variational quantum eigensolver as a quantum-assisted method for waveguide modal analysis. Starting from the Helmholtz equation for TM modes, we discretize the system using the finite difference method, map the Hamiltonian onto the Pauli basis, and implement the VQE with a hardware-efficient ansatz optimized via BFGS on the Qiskit statevector simulator of IBM [1]. As a test case, we analyze a shielded stripline. The quantum eigensolver successfully computes the first two TM modes and their cutoff frequencies while reconstructing the Ezand Exfield distributions at 1 GHz. This preliminary study shows the feasibility of quantum algorithms for solving large eigenvalue problems in computational electromagnetics where classical computing can fail, opening new possibilities for the efficient analysis of shielded multiconductor transmission lines, where higher-order modes significantly impact cross-talk and signal integrity. Future work will focus on scaling this approach to analyze multiconductor propagation in complex transmission-line structures.
The increasing complexity of modern power grids, driven by the integration of renewable energy sources, decentralized energy generation, and dynamic load variations, necessitates advanced computational approaches for efficient grid optimization. Conventional algorithms often struggle with the high-dimensionality and computational intensity of power system optimization problems, prompting the exploration of quantum computing as a transformative alternative. Quantum computing, particularly quantum machine learning (QML) and quantum optimization algorithms, has demonstrated significant potential in accelerating grid stability analysis, energy dispatch, and fault detection. This chapter provides a comprehensive investigation into quantum computing applications for power electronics, focusing on quantum-inspired machine learning models and hybrid quantum-classical frameworks for IoT-enabled smart grids. The potential advantages of quantum algorithms, including the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), and Grover’s search algorithm, are analyzed in the context of grid optimization, fault detection, and cybersecurity. Additionally, a comparative analysis of classical and quantum machine learning techniques highlights key performance differences and the challenges associated with practical quantum implementations. Despite the promising advancements, several challenges, including quantum hardware limitations, noise susceptibility, and scalability issues, must be addressed for real-world deployment. Future directions emphasize the need for noise-resilient quantum algorithms, efficient hybrid architectures, and quantum-inspired classical methods to bridge the gap between existing computational techniques and next-generation quantum solutions for power grid management.
The integration of high-penetration renewable energy introduces significant stochasticity and non-convexity into power system dispatching, challenging the computational limits of classical optimization. While Variational Quantum Algorithms (VQAs) on Noisy Intermediate-Scale Quantum (NISQ) devices offer a promising path for combinatorial acceleration, existing approaches typically treat the power grid as a "black box", suffering from poor scalability (barren plateaus) and frequent violations of physical constraints. Bridging these gaps, this paper proposes a Physics-Informed Hybrid Quantum-Classical Dispatching (PI-HQCD) framework. We construct a topology-aware Hamiltonian that explicitly embeds linearized power flow equations, storage dynamics, and multi-timescale coupling directly into the quantum substrate, significantly reducing the search space dimensionality. We further derive a noise-adaptive regularization mechanism that theoretically bounds the effective Lipschitz constant of the objective function, guaranteeing convergence stability under realistic quantum measurement noise. Numerical experiments on the IEEE 39-bus benchmark and a 118-bus regional grid demonstrate that PI-HQCD achieves superior economic efficiency and higher renewable utilization compared to stochastic dual dynamic programming (SDDP). Theoretical analysis confirms that this topology-aware design leads to an O(1/N) gradient variance scaling, effectively mitigating barren plateaus and ensuring scalability for larger networks. This work establishes a rigorous paradigm for embedding engineering physics into quantum computing, paving the way for practical quantum advantage in next-generation grid operations.
Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices-Inspired by Schur's triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver-With additional [Formula: see text] quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm's feasibility. We also undertake a comprehensive parametric study to validate VQUE's scalability, generality, and performance in realistic applications.
Advanced functionalities incorporated in the energy systems include the two-way communication feature, decentralized power generation, and the possibility to monitor operating conditions in real-time, which have already been achieved with the rapid deployment of smart grids. Nonetheless, current classical computing methods have reached severe constraints in facing the increase in complexity, massive volumes of data analysis, and intensive security demands of contemporary power grids. Quantum computation, based on the principles of superposition, entanglement, and quantum parallelism, has the transformative potential of surmounting these drawbacks. In this paper, how quantum computing can be applied to smart grid technologies in four significant areas including: (i) quantumenhanced optimization of dynamic energy distribution and unit commitment tasks, (ii) quantum machine learning to reliably forecast demand loads and renewable energy, (iii) quantum cryptography to secure communication and data verification, and (iv) quantum sensing to achieve high-fidelity fault detection and grid state monitoring is discussed. The findings point to the advantages of the use of quantum algorithms in solving complex computationally intractable optimization problems involved in grid management through near real-time solutions using quantum algorithms such as Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). The issues of noise, decoherence, hardware scalability, and hybrid quantum-classical approaches toward near-term deployment are also examined. This paper demonstrates that quantum computing has the potential to substantially improve the reliability, security, and efficiency of next-generation smart grids.