Bounds on the number of time steps for simulating arbitrary interaction graphs
Abstract
In previous papers we have considered mutual simulation of n-partite pair-interaction Hamiltonians. We have focussed on the running time overhead of general simulations, while considering the required number of time steps only for special cases (decoupling and time-reversal). These two complexity measures differ significantly. Here we derive lower bounds on the number of time steps for general simulations. In particular, the simulation of interaction graphs with irrational spectrum requires at least n steps. We discuss as examples graphs that correspond to graph codes and nearest neighbor interactions in 1- and 2-dimensional lattices. In the latter case the lower bounds are almost tight.
Keywords
Cite
@article{arxiv.quant-ph/0203061,
title = {Bounds on the number of time steps for simulating arbitrary interaction graphs},
author = {Dominik Janzing and Pawel Wocjan and Thomas Beth},
journal= {arXiv preprint arXiv:quant-ph/0203061},
year = {2007}
}
Comments
12 pages, 3 figures, some corrections of Theorem 1 and its proof