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Quantum power system state estimation (QPSSE) offers an inspiring direction for tackling the challenge of state estimation through quantum computing. Nevertheless, the current bottlenecks originate from the scarcity of practical and scalable QPSSE methodologies in the noisy intermediate-scale quantum (NISQ) era. This paper devises a NISQ−QPSSE algorithm that facilitates state estimation on real NISQ devices. Our new contributions include: (1) A variational quantum circuit (VQC)-based QPSSE formulation that empowers QPSSE analysis utilizing shallow-depth quantum circuits; (2) A variational quantum linear solver (VQLS)-based QPSSE solver integrating QPSSE iterations with VQC optimization; (3) An advanced NISQ-compatible QPSSE methodology for tackling the measurement and coefficient matrix issues on real quantum computers; (4) A noise-resilient method to alleviate the detrimental effects of noise disturbances. The encouraging test results on the simulator and real-scale systems affirm the precision, universality, and scalability of our QPSSE algorithm and demonstrate the vast potential of QPSSE in the thriving NISQ era.