  Bound states in quantum dots coupled to superconductors can be in a coherent
superposition of states with different electron number but with the same
fermion parity. Electrostatic gating can tune this superposition to a sweet
spot, where the quantum dot has the same mean electric charge independent of
its electron-number parity. Here, we propose to encode quantum information in
the local fermion parity of two tunnel-coupled quantum dots embedded in a
Josephson junction. At the sweet spot, the qubit states have zero charge dipole
moment. This protects the qubit from dephasing due to charge noise acting on
the potential of each dot, as well as fluctuations of the (weak) inter-dot
tunneling. At weak inter-dot tunneling, relaxation is suppressed because of
disjoint qubit states. On the other hand, for strong inter-dot tunneling the
system is protected against noise affecting each quantum dot separately (energy
level noise, dot-superconductor tunneling fluctuations, and hyperfine
interactions). Finally, we describe initialization and readout as well as
single-qubit and two-qubit gates by pulsing gate voltages.
