Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.
Liao, HAM-Schrödingerisation: a generic framework of quantum simulation for any nonlinear PDEs, arXiv:2406.15821 (2024)
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Quantum algorithm for the nonlinear Schr\"odinger equation via the Lax-pair scattering
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.