On the Efficiency of Quantum Algorithms for Hamiltonian Simulation

Anargyros Papageorgiou, Chi Zhang

Published 2010-05-08, updated 2010-10-11Version 3

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.