Time–optimal Hamiltonian simulation and gate synthesis using homogeneous local unitaries

Motivated by experimental limitations commonly met in the design of solid state quantum computers, we study the problems of non–local Hamiltonian simulation and non–local gate synthesis when only homogeneous local unitaries are performed in order to tailor the available interaction. Homogeneous (i.e. identical for all subsystems) local manipulation implies a more refined classification of interaction Hamiltonians than the inhomogeneous case, as well as the loss of universality in Hamiltonian simulation. For the case of symmetric two–qubit interactions, we provide time–optimal protocols for both Hamiltonian simulation and gate synthesis.