  We study a superlattice formed by tunnel-coupled identical antidots
periodically situated in a two-dimensional topological insulator placed in a
magnetic field. The superlattice spectrum can be controlled by gate electrodes
or by changing the magnetic flux through the antidots. We demonstrate that a
topologically protected qubit appears at the boundary between two regions with
different fluxes. The qubit properties depend on the value of the flux jump on
the boundary and can be controlled by the gate voltage. We derive the effective
Hamiltonian of such a qubit and analyze the dependence of its properties on the
main parameters of the superlattice: the tunnel coupling between antidots, and
the probability of jumps with the spin flip.
