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IEEE Transactions on Power Systems

Quantum Electromagnetic Transients Program

Yifan Zhou, Fei Feng, Peng Zhang

Published Mar 18, 2021• 34 citations
Publisher

Abstract

This letter devises a quantum electromagnetic transients program (QEMTP) which is the first attempt to tackle the computational challenges in solving EMTP through quantum computing. The main contributions lie in: (1) A quantum-enabled EMTP formulation with Dommel's model encoded in quantum states; 2) An Harrow-Hassidim-Lloyd (HHL)-based QEMTP to solve the discrete-time nodal equations; 3) An iteration-based HHL revision for mitigating temporal errors to achieve high accuracy of QEMTP with limited quantum resources. Case studies verify the correctness and efficacy of QEMTP in simulating both fast and slow dynamics.

DOI
10.1109/tpwrs.2021.3067207

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This letter devises a quantum electromagnetic transients program (QEMTP) which is the first attempt to tackle the computational challenges in solving EMTP through quantum computing. The main contributions lie in: (1) A quantum-enabled EMTP formulation with Dommel's model encoded in quantum states; 2) An Harrow-Hassidim-Lloyd (HHL)-based QEMTP to solve the discrete-time nodal equations; 3) An iteration-based HHL revision for mitigating temporal errors to achieve high accuracy of QEMTP with limited quantum resources. Case studies verify the correctness and efficacy of QEMTP in simulating both fast and slow dynamics.
Quantum-empowered electromagnetic transients program (QEMTP) is a promising paradigm for tackling EMTP’s computational burdens. Nevertheless, no existing studies truly achieve a practical and scalable QEMTP operable on today’s noisy-intermediate-scale quantum (NISQ) computers. The strong reliance on noise-free and fault-tolerant quantum devices–which appears to be decades away– hinder practical applications of current QEMTP methods. This paper devises a NISQ-QEMTP methodology which for the first time transitions the QEMTP operations from ideal, noise-free quantum simulators to real, noisy quantum computers. The main contributions lie in: (1) design of shallow-depth QEMTP quantum circuits for mitigating noises on NISQ quantum devices; (2) practical QEMTP linear solvers incorporating executable quantum state preparation and measurements for nodal voltage computations; (3) a noise-resilient QEMTP algorithm leveraging quantum resources logarithmically scaled with power system dimension; (4) a quantum shifted frequency analysis (QSFA) for accelerating QEMTP by exploiting dynamic phasor simulations with larger time steps; (5) a systematical analysis on QEMTP’s performance under various noisy quantum environments. Extensive experiments systematically verify the accuracy, efficacy, universality and noise-resilience of QEMTP on both noise-free simulators and IBM real quantum computers.
In modern power systems, the integration of converter-interfaced generations requires the development of electromagnetic transient network simulation programs (EMTP) that can capture rapid fluctuations. However, as the power system scales, the EMTP's computing complexity increases exponentially, leading to a curse of dimensionality that hinders its practical application. Facing this challenge, quantum computing offers a promising approach for achieving exponential acceleration. To realize this in noisy intermediate-scale quantum computers, the variational quantum linear solution (VQLS) was advocated because of its robustness against depolarizing noise. However, it suffers data inflation issues in its preprocessing phase, and no prior research has applied quantum computing to high-frequency switching EMT networks.To address these issues, this paper first designs the matrix low-dimension qubit casting (MLQC) method to address the data inflation problem in the preprocessing of the admittance matrix for VQLS in EMT networks. Besides, we propose a real-only quantum circuit reduction method tailored to the characteristics of the EMT network admittance matrices. Finally, the proposed quantum EMTP algorithm (QEMTP) has been successfully verified for EMT networks containing a large number of high-frequency switching elements.
This letter is a proof of concept for quantum power flow (QPF) algorithms which underpin various unprecedentedly efficient power system analytics exploiting quantum computing. Our contributions are three-fold: 1) Establish a quantum-state-based fast decoupled model empowered by Hermitian and constant Jacobian matrices; 2) Devise an enhanced Harrow-Hassidim-Lloyd (HHL) algorithm to solve the fast decoupled QPF; 3) Further improve the HHL efficiency by parameterizing quantum phase estimation and reciprocal rotation only at the beginning stage. Promising test results validate the accuracy and efficacy of QPF and demonstrate QPF's enormous potential in the era of quantum computing.
Quantum computing is a potential approach for addressing computational challenges in solving electromagnetic problems. A quantum method, called the Harrow/Hassidim /Lloyd (HHL) algorithm has recently been applied to solve the equations from finite-element-method (FEM) formulation of electromagnetic problems. Here we address a further step in this direction. Since quantum state vectors always have unit norm, the solution vector from HHL is only proportional to the final electromagnetic solutions. The magnitude of the final electromagnetic solution vector remains unavailable from HHL In this paper, a new quantum formulation is proposed to find the magnitude of the final electromagnetic solutions. The proposed method can be used to scale the HHL results to the correct magnitude of electromagnetic solutions. In this way, the proposed method is a further advance in making the quantum computing more effective in solving electromagnetic problems.
Quantum simulation of electromagnetic (EM) structures is still in its infancy. In this paper, we investigate the possibility of applying quantum computing to solve the finite element equations for EM problems. Specifically, we propose to leverage a milestone in quantum computing, i.e., the Harrow/Hassidim/Lloyd (HHL) algorithm, to solve the finite element equations in the EM domain. To do this, we first present a systematic method to reformulate the finite element equations into quantum computation format and apply the HHL algorithm to solve the new equations. Taking advantage of the special properties of finite element matrices in EM problems, we then devise a stepwise algorithm to efficiently determine the suitable values for the hyperparameters of HHL. The proposed method can in theory solve the EM finite element equations in logarithmic time relative to the size of the finite element matrix. This is exponentially faster than that achievable by classical computation as the matrix size increases. A two-dimensional EM example is used to illustrate how the proposed method can be used to find the solutions to EM problems through quantum computation.
Computational electromagnetics plays a central role in many industrial applications but often requires substantial computational resources, particularly when fine spatial discretizations are needed. While classical approaches remain the standard, quantum computing offers the potential to accelerate large-scale simulations by encoding them with a limited number of qubits. Here, we investigate the performance and resource scaling of the Harrow-Hassidim-Lloyd (HHL) and Quantum Singular Value Transformation (QSVT) algorithms for solving linear systems generated by the finite-difference time-domain (FDTD) method, a widely adopted numerical scheme for discretizing Maxwell's equations. We benchmark their performance across representative industrial use cases, including radar propagation, lens simulations, and beamforming processes. Our results demonstrate the validity of the approaches, achieving state infidelities smaller than 2⋅10−32\cdot 10^{-3}2⋅10−3 with success probabilities greater than 10−310^{-3}10−3, compatible with practical quantum state sampling. Overall, we observe that the QSVT method consistently delivers higher accuracy. We further observe that the condition number of the linear matrix, a key factor governing the performance of quantum solvers, saturates as the number of spatial lattice points increases. This implies that the spatial grid can be scaled to realistic industrial dimensions without increasing the HHL or QSVT circuit depth due to ill-conditioned matrices.