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2025-11-29
Variational Quantum Algorithm for Photonic Crystals(Invited Paper)
By
Progress In Electromagnetics Research, Vol. 184, 1-13, 2025
Abstract
Photonic crystals (PhCs) play a crucial role in describing the quantized collective behavior of wave functions. However, the existing investigations into their eigenstates primarily rely on classical computational methods. Variational quantum algorithm (VQA) represents a promising quantum computing technology that can be implemented on noisy intermediate-scale quantum (NISQ) devices, potentially surpassing the classical computational capabilities. Here, we propose a method to analyze the band and eigenstate properties of PhCs based on variational quantum eigensolver (VQE). We firstly reformulate the Maxwell's equations into a Hermitian generalized eigenvalue problem. By appropriately selecting a loss function and employing the proposed quantum eigenvalue solver, we successfully obtain the generalized eigenvalues using a quantum gradient descent algorithm. To validate our approach, we perform simulations on two prototypical PhCs in square and hexagonal lattices. The results demonstrate that a complex Ansatz can effectively capture the optimal solution, successfully yielding the generalized eigenvalues, but a simpler Ansatz exhibits significant limitations. Our findings provide new insights into the application of VQAs in PhCs and other quantum topological systems.
Citation
Long Chen, Xinyu Li, Jianlin Su, Siqi Huang, Zixuan Cai, Zhicai Yu, Yuming Ning, Qiang Xiao, Jianan Zhang, Qian Ma, Zhihao Lan, Jianwei You, and Tie-Jun Cui, "Variational Quantum Algorithm for Photonic Crystals(Invited Paper)," Progress In Electromagnetics Research, Vol. 184, 1-13, 2025.
doi:10.2528/PIER25081203
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