2002/03/14 by Dominik Janzing, Janzing, Dominik, Pawel Wocjan +3
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0203061
12 pages, 3 figures, some corrections of Theorem 1 and its proof
openalex publication_date 2002/03/14 · arxiv created 2002/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.