Simulating Sparse Hamiltonians with Star Decompositions
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 (d2(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 (d4(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.
Unable to display preview. Download preview PDF.