Matrix Low-dimensional Qubit Casting Based Quantum Electromagnetic Transient Network Simulation Program

TL;DR

This work addresses the exponential complexity of electromagnetic transient network simulation (EMTP) by introducing a matrix low-dimensional qubit casting (MLQC) framework to enable scalable quantum EMTP (QEMTP) on noisy intermediate-scale quantum devices. It combines a generalized Kronecker decomposition (GKD) to obtain low-dimensional Kronecker factors, a real-only Pauli-mapping circuit to reduce quantum resources, and a fixed-admittance switch model (FASM) to handle high-speed switching without topology blow-up. The proposed approach yields lossless or near-lossless matrix mapping with substantial circuit reductions and demonstrates accurate, fast simulations for both DC-DC and AC-DC EMT networks, achieving significant speedups and enabling practical QEMTP on current quantum hardware. The results indicate MLQC-based QEMTP can dramatically lower preprocessing and circuit-depth costs while maintaining high fidelity, suggesting practical impact for quantum-accelerated EMTP in power systems with fast-switching devices.

Abstract

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.

Figures (12)

• Figure 1: The EMTP model for RLC components. By discretizing the voltage and current equations of each electrical component in the network using the trapezoidal method, the final EMTP equivalent network can be constructed for the basic RLC components.
• Figure 2: Plot for the structure of the hardware-efficient variational quantum circuit. The figure presents the ansatz circuit with qubits number $n=6$. The structure inside the dashed box represents one ansatz layer that includes controlled-Z gates and rotation gates $R_{y}$. By optimizing the rotation angle parameters $\alpha$ in gates $R_{y}$, the circuit can express the desired quantum state. The performances of the circuit can be improved by stacking multiple ansatz layers. The circuit shown in the figure consists of $3$ ansatz layers in series.
• Figure 3: The Bloch sphere representation of the projection of $|\Phi\rangle$ onto $|i\rangle$ in the case of a single qubit. The red line represents the initial, unoptimized state $|\Phi\rangle$, while the blue line represents the target state $|i\rangle$. In the beginning, the projection distance between two quantum states is very small. When $|\Phi\rangle$ and $|i\rangle$ are perpendicular, the projection distance is zero. After optimizing the parameter $\alpha$ in the variational circuit, $|\Phi\rangle$ and $|i\rangle$ nearly overlap under the optimal parameters $\alpha_{opt}$, and the projection distance becomes 1.
• Figure 4: Plot for the Hadamard test quantum circuit for calculating $\delta_{ii^{\prime}j}$ under the case of $j=1$. The circuit calculates the expectation value of the Hamiltonian by measuring the probability information of the first qubit, a.k.a. auxiliary qubit. Specifically, the real part of $\delta_{ii^{\prime}j}$ is determined by $P(0)-P(1)$. To compute the imaginary part, an $S$-gate is added to the auxiliary qubit. Then, the same procedure for the real part is conducted. For the calculation of $\beta_{ii^{\prime}}$, it is only necessary to remove the unitary $U$ and $Z_{j}$ gate from the circuit.
• Figure 5: The schematic diagram of the MLQC algorithm framework.

Theorems & Definitions (7)

• Remark 1
• Theorem 1: Uniqueness of the matrix mapping
• Remark 2
• Theorem 2: Y-Gate Even Principle for Pauli Mapping of Real Symmetric Matrices
• proof
• Remark 3
• Remark 4