A quantum algorithm for linear MHD stability analysis

A key question in magnetically confined fusion is that of the stability of the confined plasma to ideal-MHD modes. Answering this question for equilibria without background flows boils down to solving a generalized eigenvalue problem involving a Hermitian matrix. By reducing this problem to ground energy estimation, we develop a quantum algorithm that yields a polynomial speedup with respect to the number of grid points for two- and three-dimensional MHD equilibria. The performance of our algorithm hinges on a proper treatment of the continuous Hermitian operator, such that its discretization remains Hermitian. A byproduct of the discretization is the appearance of spurious eigenvalues, which need to be treated carefully. To demonstrate the efficacy of the approach, we show classical numerical results for well-known one-dimensional equilibria, such as magnetized slabs as well as the theta and Z pinches.