  Magnetic impurities in $s$-wave superconductors lead to spin-polarized
Yu-Shiba-Rusinov (YSR) in-gap states. Chains of magnetic impurities offer one
of the most viable routes for the realization of Majorana bound states which
hold a promise for topological quantum computing. However, this ambitious goal
looks distant since no quantum coherent degrees of freedom have yet been
identified in these systems. To fill this gap we propose an effective two-level
system, a YSR qubit, stemming from two nearby impurities. Using a
time-dependent wave-function approach, we derive an effective Hamiltonian
describing the YSR qubit evolution as a function of distance between the
impurity spins, their relative orientations, and their dynamics. We show that
the YSR qubit can be controlled and read out using the state-of-the-art
experimental techniques for manipulation of the spins. Finally, we address the
effect of the spin noises on the coherence properties of the YSR qubit, and
show a robust behaviour for a wide range of experimentally relevant parameters.
Looking forward, the YSR qubit could facilitate the implementation of a
universal set of quantum gates in hybrid systems where they are coupled to
topological Majorana qubits.
