@article {1223,
title = {Simulating sparse Hamiltonians with star decompositions},
year = {2010},
month = {2010/03/18},
abstract = { We present an efficient algorithm for simulating the time evolution due to a
sparse Hamiltonian. In terms of the maximum degree d and dimension N of the
space on which the Hamiltonian H acts for time t, this algorithm uses
(d^2(d+log* N)||Ht||)^{1+o(1)} queries. This improves the complexity of the
sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders,
which scales like (d^4(log* N)||Ht||)^{1+o(1)}. To achieve this, we decompose a
general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of
non-zero entries have the property that every connected component is a star,
and efficiently simulate each of these pieces.
},
doi = {10.1007/978-3-642-18073-6_8},
url = {http://arxiv.org/abs/1003.3683v2},
author = {Andrew M. Childs and Robin Kothari}
}