  Power system dynamics are generally modeled by high dimensional nonlinear
differential-algebraic equations (DAEs) given a large number of components
forming the network. These DAEs' complexity can grow exponentially due to the
increasing penetration of distributed energy resources, whereas their
computation time becomes sensitive due to the increasing interconnection of the
power grid with other energy systems. This paper demonstrates the use of
quantum computing algorithms to solve DAEs for power system dynamic analysis.
We leverage a symbolic programming framework to equivalently convert the power
system's DAEs into ordinary differential equations (ODEs) using index reduction
methods and then encode their data into qubits using amplitude encoding. The
system nonlinearity is captured by Hamiltonian simulation with truncated Taylor
expansion so that state variables can be updated by a quantum linear equation
solver. Our results show that quantum computing can solve the power system's
DAEs accurately with a computational complexity polynomial in the logarithm of
the system dimension. We also illustrate the use of recent advanced tools in
scientific machine learning for implementing complex computing concepts, i.e.
Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with
abstract representation for power engineering applications.
