Approximating Hamiltonian dynamics with the Nyström method

@article{Rudi2020ApproximatingHD,
  title={Approximating Hamiltonian dynamics with the Nystr{\"o}m method},
  author={Alessandro Rudi and Leonard Wossnig and Carlo Ciliberto and Andrea Rocchetto and Massimiliano Pontil and Simone Severini},
  journal={ArXiv},
  year={2020},
  volume={abs/1804.02484}
}
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum… 
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