We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{ j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number of exponentials required to approximate $e^{ -iHt}$ with error $\e$. Moreover, we derive the order of the splitting method that optimizes the cost of the resulting algorithm. We show significant speedups relative to previously known results.
Categories: quant-ph