  We propose a universal gate set acting on a qubit formed by the degenerate
ground states of a Coulomb-blockaded time-reversal invariant topological
superconductor island with spatially separated Majorana Kramers pairs: the
"Majorana Kramers Qubit". All gate operations are implemented by coupling the
Majorana Kramers pairs to conventional superconducting leads. Interestingly, in
such an all-superconducting device, the energy gap of the leads provides
another layer of protection from quasiparticle poisoning independent of the
island charging energy. Moreover, the absence of strong magnetic fields - which
typically reduce the superconducting gap size of the island - suggests a unique
robustness of our qubit to quasiparticle poisoning due to thermal excitations.
Consequently, the Majorana Kramers Qubit should benefit from prolonged
coherence times and may provide an alternative route to a Majorana-based
quantum computer.
