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About this paper
Dylan Herman, Jacob Watkins, Guneykan Ozgul, Jiayu Shen, Brandon Augustino, Junhyung Lyle Kim, Shouvanik Chakrabarti
The authors develop digital simulation methods for Schrödinger dynamics on curved spaces, where the Laplace–Beltrami operator governs kinetic energy. They use global spectral bases for selected geometries and local charts under explicit assumptions. For a spatially discretized nonlinear sigma model, they prove error O(epsilon) and success probability at least 1−O(epsilon), with resources polynomial in lattice sites and 1/epsilon under fixed parameters; this is not a speedup result.
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