  The simulation of quantum systems is one of the most promising applications
of quantum computers. In this paper we present a quantum algorithm to perform
digital quantum simulations of the BCS model on a quantum register with a star
shaped connectivity map, as it is, e.g., featured by color centers in diamond.
We show how to effectively translate the problem onto the quantum hardware and
implement the algorithm using only the native interactions between the qubits.
Furthermore we discuss the complexity of the circuit. We use the algorithm to
simulate the dynamics of the BCS model by subjecting its mean-field ground
state to a time-dependent perturbation. The quantum simulation algorithm is
studied using a classical simulation.
