TY - JOUR
T1 - Simulating sparse Hamiltonians with star decompositions
Y1 - 2010
A1 - Andrew M. Childs
A1 - Robin Kothari
AB - 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.
UR - http://arxiv.org/abs/1003.3683v2
J1 - Theory of Quantum Computation
U5 - 10.1007/978-3-642-18073-6_8
ER -