Exact simulation of multi-qubit dynamics with only three qubits

We present equivalence relations which simplify the dynamics of an important class of interacting multi-qubit systems. We show that a wide class of M + 1 qubit systems, with one or M excitations, can be reduced to an equivalent n + 1 qubit system with n >= 2, for any M. The equivalent system faithfully reproduces the overall dynamics of the original one including the entanglement properties. In addition to its direct application to qubit-cavity systems, the formalism offers insight into a variety of situations ranging from decoherence due to a spin-bath with its own internal entanglement, through to energy transfer processes in organic systems such as biological photosynthetic units.