  Quantum computing, leveraging principles of quantum mechanics, represents a
transformative approach in computational methodologies, offering significant
enhancements over traditional classical systems. This study tackles the complex
and computationally demanding task of simulating power system transients
through solving differential algebraic equations (DAEs). We introduce two novel
Quantum Neural Networks (QNNs): the Sinusoidal-Friendly QNN and the
Polynomial-Friendly QNN, proposing them as effective alternatives to
conventional simulation techniques. Our application of these QNNs successfully
simulates two small power systems, demonstrating their potential to achieve
good accuracy. We further explore various configurations, including time
intervals, training points, and the selection of classical optimizers, to
optimize the solving of DAEs using QNNs. This research not only marks a
pioneering effort in applying quantum computing to power system simulations but
also expands the potential of quantum technologies in addressing intricate
engineering challenges.
