  Quantum power flow (QPF) provides inspiring directions for tackling power
flow's computational burdens leveraging quantum computing. However, existing
QPF methods are mainly based on noise-sensitive quantum algorithms, whose
practical utilization is significantly hindered by the limited capability of
today's noisy-intermediate-scale quantum (NISQ) devices. This paper devises a
NISQ-QPF algorithm, which enables power flow calculation on noisy quantum
computers. The main contributions include: (1) a variational quantum circuit
(VQC)-based AC power flow formulation, which enables QPF using short-depth
quantum circuits; (2) noise-resilient QPF solvers based on the variational
quantum linear solver (VQLS) and modified fast decoupled power flow; (3) a
practical NISQ-QPF framework for implementable and reliable power flow analysis
on noisy quantum machines. Promising case studies validate the effectiveness
and accuracy of NISQ-QPF on IBM's real, noisy quantum devices.
