Digital quantum simulation of the BCS model with a central-spin-like quantum processor

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 (reduced) Bardeen-CooperSchrieffer (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.