  We consider an electron confined in a gated nanowire quantum dot (NQD) with
arbitrarily strong spin-orbit coupling (SOC) and weak static magnetic field,
and treat the latter as a perturbation to seek the maximal spin-motion
entangled states with the exact general solutions of the perturbed equations.
From the boundedness and self-consistent conditions of the general solutions we
find two corrected energies to any n level of the unperturbed system with
ground state n = 0, which are much less than the unperturbed level-difference
and corresponds to a spin-orbit qubit. We demonstrate the metastability of the
two-level states and the decoherence-averse effect of SOC, and suggest an
alternative scheme to perform the qubit control, simply by adjusting the
orientation of magnetic field for any fixed SOC. Such a adjustment can lead to
the spin flipping of the state vector and the position exchanging of the
probability-density wavepackets which can be proposed as the non-Abelian
quasiparticles. The results could be directly extended to a weakly coupled
array of NQDs for coherently encoding the robust spin-orbit qubits.
