Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limitations on the simulation of non-sparse Hamiltonians   The problem of simulating sparse Hamiltonians on quantum computers is well
studied. The evolution of a sparse N x N Hamiltonian H for time t can be
simulated using O(||Ht||poly(log N)) operations, which is essentially optimal
due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians
and show significant limitations on their simulation. We generalize the
no--fast-forwarding theorem to dense Hamiltonians, ruling out generic
simulations taking time o(||Ht||), even though ||H|| is not a unique measure of
the size of a dense Hamiltonian $H$. We also present a stronger limitation
ruling out the possibility of generic simulations taking time poly(||Ht||,log
N), showing that known simulations based on discrete-time quantum walk cannot
be dramatically improved in general. On the positive side, we show that some
non-sparse Hamiltonians can be simulated efficiently, such as those with graphs
of small arboricity.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph