On the Efficiency of Quantum Algorithms for Hamiltonian Simulation

Abstract

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 $\text{e}$. 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.