A quantum computational approach to linear MHD stability analysis

For any magnetically confined fusion reactor configuration, the foremost question we must answer is whether the configuration possesses linear MHD stability. Answering this question involves linearizing the ideal MHD equations about the equilibrium, thereby obtaining a generalized eigenvalue problem. Such a problem involves a matrix whose dimension scales polynomially in the spatial precision, and exponentially in the number of spatial dimensions. Our situation suffers from the "curse of dimensionality." We propose a quantum algorithm using block-encoding and phase estimation which solves this eigenvalue problem for the well-known theta pinch, Z pinch, and the screw pinch. We show that the quantum algorithm can potentially yield a polynomial speedup in system size in higher dimensions. Whether an exponential speedup in system size is possible remains an open problem.