Necessary conditions for efficient simulation of Hamiltonians using local unitary operations

We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are based on the algebraic-geometric invariants introduced in [1-2], but independent of the eigenvalues of Hamiltonians. Our results indicate that the problem of efficient simulation of Hamiltonians for arbitrary bipartite or multipartite quantum systems cannot be described by using only eigenvalues, unlike that in the two-qubit case.