Exponential improvement in precision for simulating sparse Hamiltonians

@article{Berry2014ExponentialII,
  title={Exponential improvement in precision for simulating sparse Hamiltonians},
  author={D. Berry and Andrew M. Childs and R. Cleve and Robin Kothari and R. Somma},
  journal={Proceedings of the forty-sixth annual ACM symposium on Theory of computing},
  year={2014}
}
  • D. Berry, Andrew M. Childs, +2 authors R. Somma
  • Published 2014
  • Computer Science, Physics, Mathematics
  • Proceedings of the forty-sixth annual ACM symposium on Theory of computing
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a d-sparse Hamiltonian H on n qubits can be simulated for time t with precision ε using O(τlog(τ/ε)/log log(τ/ε)) queries and O(τnlog2(τ/ε)/log log(τ/ε)) additional 2-qubit gates, where τ=d2||H||maxt. Unlike previous approaches based on product formulas, the query complexity is… Expand
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