Quantum Shifted Frequency Analysis through Krylov Subspace Decomposition

This paper develops a quantum Krylov subspace (QKS)-based shifted frequency analysis (SFA) approach, which synergizes the SFA-enabled acceleration with quantum subspace-enabled scalability to facilitate ultra-scalable electromagnetic transient studies. Our innovations are threefold: (1) We develop a QKS-based SFA architecture, which enables solving high-dimensional SFA models in a lower-dimensional subspace spanned by quantum basis vectors; (2) We design QKS basis vectors that can effectively preserve the critical information of SFA models within the quantum Krylov subspace while maintaining robustness against ill-conditioned matrices; (3) We construct quantum projection and reconstruction circuits to implement QKS with manageable circuit scales. Extensive experiments in IEEE standard testing systems demonstrate the accuracy and effectiveness of QKS-based SFA and its advantage over existing methods. This work, for the first time, unlocks the potential of quantum subspaces in power grid analytics and successfully realizes quantum-based SFA on real-scale power grids.