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What interactions are sufficient to simulate arbitrary quantum dynamics in acomposite quantum system? Dodd et al. (quant-ph/0106064) provided a partialsolution to this problem in the form of an efficient algorithm to simulate anydesired two-body Hamiltonian evolution using any fixed two-body entanglingN-qubit Hamiltonian, and local unitaries. We extend this result to the casewhere the component systems have D dimensions. As a consequence we explain howuniversal quantum computation can be performed with any fixed two-bodyentangling N-qudit Hamiltonian, and local unitaries.Comment: 13 pages, an error in the "Pauli-Euclid-Gottesman Lemma" fixed, main  results unchange

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces