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 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.
Current quantum computers (QCs) belong to the noisy intermediate-scale quantum (NISQ) class, characterized by noisy qubits, limited qubit capabilities, and limited circuit depth. These limitations have led to the development of hybrid quantum-classical algorithms that split the computational cost between classical and quantum hardware. Among the hybrid algorithms, the variational quantum eigensolver (VQE) is mentioned. The VQE is a variational quantum algorithm designed to estimate the eigenvalues and eigenvectors of a system on universal-gate quantum architectures. A canonical problem in electromagnetics is the computation of eigenmodes within waveguides. Following the finite difference method, the wave equation can be recast as an eigenvalue problem. This work exploits the quantum superposition and entanglement in quantum computing to solve the square waveguide mode problem. This algorithm is expected to demonstrate exponentially efficiency over classical computational techniques as the qubit count increases. The simulations were performed on IBM’s three-qubit quantum simulator, Qasm IBM Simulator. A shot-based simulation was performed considering computationally based measurements of the quantum hardware. The results of the probabilistic read-out, reported in terms of 2-D eigenmode field distributions, are close to ideal values with a few number of qubits, confirming the possibility to exploit the quantum advantage to formulate innovative eigensolvers.
The advent of noisy intermediate-scale quantum (NISQ) systems signifies an important stage in quantum computing development. Despite the constraints due to their limited qubit numbers and noise susceptibility, NISQ devices exhibit substantial potential to tackle complex computational challenges via hybrid classical-quantum algorithms. Among the various hybrid algorithms, variational quantum algorithms (VQAs) are gaining increasing attention due to their ability to solve highly complex, large-scale problems where classical algorithms fail. In particular, the variational quantum eigensolver (VQE) shows its potential in calculating the energies and ground states of large systems, where the complexity of solving such problems grows exponentially and becomes intractable for classical computers. At this regard, the aim of this paper is to extend the use of VQE for solving circular waveguide modes to verify their applicability to mathematically complex EM problems. In particular, we propose to calculate the fundamental and the some higher order modes for both transverse electric and transverse magnetic cases in circular waveguides. This is mathematically challenging due to the nature of geometry and the associated boundary conditions of circular structures. The results confirm the possibility of applying VQE for mathematically complex EM problems, announcing its potential to scale up and solve high-dimensional, large-scale EM problems where classical algorithms can fail.
Current NIQST machines have a relatively small number of qubits and a limited circuit depth. In this regard, a class of quantum variational algorithms (VQAs) have been developed to be able to split the computational cost between classical and quantum hardware. In this study, the VQE algorithm has been used in order to solve the problem of propagation modes in rectangular waveguides described analytically by the Helmholtz partial differential equation. The IBM quantum device called manila was used in these calculations to provide noise present in physical hardware. In order to implement the VQE, IBM's proprietary framework called Qiskit has been used. The results show good agreement between calculations run on simulated quantum hardware and those run on real quantum hardware. This agreement between theory and experiment is evidence that high fidelity modeling of electromagnetic fields utilizing quantum hardware is possible.
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.
Quantum computing has the potential to revolutionize computational problem-solving by leveraging the quantum mechanical phenomena such as superposition and entanglement, enabling fundamentally different computational strategies compared to classical computing. Classical methods for solving complex and high dimensional partial differential equations (PDEs), crucial for modeling diverse physical phenomena, suffer from an exponential growth in computational complexity known as the curse of dimensionality. This can limit their effectiveness for certain high-resolution simulations and real-time computational applications. In contrast, quantum computing inherently exploits superposition and entanglement to efficiently represent and simultaneously manipulate large-scale discretized PDEs, using exponentially fewer resources compared to classical systems. There are currently many quantum techniques available for solving partial differential equations (PDEs), which are mainly based on variational quantum circuits. However, the existing quantum PDE solvers, particularly those based on variational quantum eigensolver (VQE) techniques, suffer from several limitations. These include low accuracy, high execution times, and low scalability on quantum simulators as well as on noisy intermediate-scale quantum (NISQ) devices, especially for multidimensional PDEs. In this work, we propose an efficient and scalable algorithm for solving multidimensional PDEs. We present two variants of our algorithm: the first leverages finite-difference method (FDM), classical-to-quantum (C2Q) encoding, and numerical instantiation, while the second employs FDM, C2Q, and column-by-column decomposition (CCD). Both variants are designed to enhance accuracy and scalability while reducing execution times. We have validated and evaluated our proposed concepts using a number of case studies including multidimensional Poisson equation, multidimensional heat equation, Black Scholes equation for financial option pricing, and Navier-Stokes equation for computational fluid dynamics (CFD), achieving promising results. Our results demonstrate higher accuracy, higher scalability, and faster execution times compared to VQE-based solvers on noise-free and noisy quantum simulators from IBM. Additionally, we validated our approach on hardware emulators and actual quantum hardware, employing noise mitigation techniques. This work establishes a practical and effective approach for solving PDEs using quantum computing for engineering and scientific applications.
Variational quantum algorithms (VQAs) are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a VQA in conjunction with the finite difference method for the calculation of propagation modes of an electromagnetic wave in a hollow metallic waveguide. The two-dimensional (2-D) waveguide problem, described by the Helmholtz equation, is approximated by a system of linear equations, whose solutions are expressed in terms of simple quantum expectation values that can be evaluated efficiently on quantum hardware. Numerical examples are presented to validate the proposed method for solving 2-D waveguide problems.