Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the number of time steps for simulating arbitrary interaction
  graphs   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.

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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas