What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.
Given a time-independent Hamiltonian H , one can construct a time-dependent Hamiltonian Ht by means of the gauge transformation Ht=UtHUt†−iUt∂tUt† . Here Ut is the unitary transformation that relates the solutions of the corresponding Schrödinger equations. In the many-body case one is usually interested in Hamiltonians with few-body (often, at most two-body) interactions. We refer to such Hamiltonians as physical. We formulate sufficient conditions on Ut ensuring that Ht is physical as long as H is physical (and vice versa). This way we obtain a general method for finding pairs of physical Hamiltonians Ht and H such that the driven many-body dynamics governed by Ht can be reduced to the quench dynamics due to the time-independent H . We apply this method to a number of many-body systems. First we review the mapping of a spin system with isotropic Heisenberg interaction and arbitrary time-dependent magnetic field to a time-independent system without a magnetic field [F. Yan, L. Yang, and B. Li, Phys. Lett. A 251, 289–293; 259, 207–211 (1999)]. Then we demonstrate that essentially the same gauge transformation eliminates an arbitrary time-dependent magnetic field from a system of interacting fermions. Further, we apply the method to the quantum Ising spin system and a spin coupled to a bosonic environment. We also discuss a more general situation where H=Ht is time-dependent but dynamically integrable.
We conduct a systematic investigation of the nuclear collective dynamics that emerges in systems with two-body random interactions. We explore the development of the mean field and study its geometry. We investigate multipole collectivities in the many-body spectra and their dependence on the underlying two-body interaction Hamiltonian. The quadrupole-quadrupole interaction component appears to be dynamically dominating in the two-body random ensemble. This quadrupole coherence leads to rotational spectral features and thus suggests the formation of the deformed mean-field of a specific geometry.