Hamiltonian simulation with optimal sample complexity

@article{Kimmel2016HamiltonianSW,
  title={Hamiltonian simulation with optimal sample complexity},
  author={Shelby Kimmel and Cedric Yen-Yu Lin and Guang Hao Low and Maris A. Ozols and Theodore J. Yoder},
  journal={npj Quantum Information},
  year={2016},
  volume={3},
  pages={1-7}
}
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631–633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal… 
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