Relaxation and decoherence of qubits encoded in collective states of engineered magnetic structures

The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of $T_{1}$ and $T_{2}$ characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, including a collective spin, a setup implementing a decoherence-free subspace, and two examples of spin chains. Our work contributes to the comprehensive understanding of the relaxation and decoherence processes and shows the advantages of the implementation of a decoherence free subspace in these setups.